Final Presentation：財務時間序列
Albert
2018年5月22日
原先構想
比較2017年世界最大的兩大科技公司(apple 與 Facebook)的報酬率的時間數列。
但是針對解釋變數部分，我找了不少網站，在R裡似乎沒有直接可以抓取我想要的資料指令，例如我的解釋變數要有
1.market value(市場價值) 2. P/B ratio(股價淨值比) 3.EPS(每股盈餘)
會想要找這三個解釋變數主要理由分別列至下方，
1.market value(市場價值) => 理由1：公司的大小與其股票報酬率高低呈反向關系
2.P/B ratio(股價淨值比) => 理由2：P/B比率越高，表示公司財務狀況越健康(風險低)，P/B比率越低(如低於一，像水餃股一樣)，表示公司有財務危機(風險高)，因此，「P/B比率」高低也與股票報酬率高低呈反向關係
3.EPS(每股盈餘) => 理由3：每股盈餘也能解釋報酬率
因為EPS是每月公布，我從TEJ抓到資料有限只有108筆，於是我就更改報告方向。
後來想一想其實可以透過getFinancial去抓財報裡資料，P/B ratio計算不易，於是打消這個念頭。
折衷作法
屈就於資料取得不易、資料整理耗時，但我還是想做 Apple 與 Facebook關聯， 這篇報導Facebook、Apple、Amazon、Google四大科技巨頭中，誰最不容易被顛覆？提到Facebook、Apple、Amazon、Google四大科技巨頭中(FAAG)，於是我以APPLE為主，Facebook、Amazon、Google為解釋變數，透過財務時間序列模型去做分析
R Packsges
- quantmod
- rugarch
- car + MASS
- ggplot2 + plotly + gridExtra
- copula
- rmgarch
操作過程
- 抓取資料並計算報酬率
rm(list=ls(all=TRUE)) #清除所有變數
library(quantmod)
library(rugarch)
library(car)
library(MASS)
library(ggplot2)
library(plotly)
library(gridExtra)
library(moments)
library(ggthemes)
start='2015-01-01'
end = "2017-12-31"
APPLE = getSymbols("AAPL",from=start,to=end, src = "yahoo", auto.assign = FALSE )
Asset = TTR::ROC(Ad(APPLE),type="continuous") #計算報酬率
colnames(Asset) = "LogReturn" #改名字
Asset = na.omit(Asset) #刪除missing的資料
Asset_mean = mean(Asset$LogReturn)
Asset_sd = sqrt(var(Asset$LogReturn))
Asset_sd = Asset_sd[1,1]關心資料基本型態
- 建構一個表：損失巨大、負報酬、正報酬、賺取巨大的機率
Asset_Basic = Asset
length(Asset$LogReturn)[1] 754Asset_mean = mean(Asset$LogReturn)
Asset_sd = sqrt(var(Asset$LogReturn))
Asset_sd = Asset_sd[1,1]
Asset_Basic$CountBigLoss= NA
Asset_Basic$NegativeReturn = NA
Asset_Basic$PositiveReturn = NA
Asset_Basic$CountBigGain= NA
d=1.5
for(i in 1:length(Asset_Basic$LogReturn)){
if(Asset_Basic$LogReturn[i]<= Asset_mean - d*Asset_sd){
Asset_Basic$CountBigLoss[i] = 1}else {
Asset_Basic$CountBigLoss[i] = 0}
}
for(i in 1:length(Asset_Basic$LogReturn)){
if(Asset_Basic$LogReturn[i]< 0){
Asset_Basic$NegativeReturn[i] = 1}else {
Asset_Basic$NegativeReturn[i] = 0}
}
for(i in 1:length(Asset_Basic$LogReturn)){
if(Asset_Basic$LogReturn[i]>= 0){
Asset_Basic$PositiveReturn[i] = 1}else {
Asset_Basic$PositiveReturn[i] = 0}
}
for(i in 1:length(Asset_Basic$LogReturn)){
if(Asset_Basic$LogReturn[i]>= Asset_mean + d*Asset_sd){
Asset_Basic$CountBigGain[i] = 1}else {
Asset_Basic$CountBigGain[i] = 0}
}
BigLossProb = sum(Asset_Basic$CountBigLoss)/length(Asset_Basic$LogReturn)
NegativeReturnProb = sum(Asset_Basic$NegativeReturn)/length(Asset_Basic$LogReturn)
PositiveReturnProb = sum(Asset_Basic$PositiveReturn)/length(Asset_Basic$LogReturn)
BigGainProb = sum(Asset_Basic$CountBigGain)/length(Asset_Basic$LogReturn)
BasicStat = matrix(
c(BigLossProb, NegativeReturnProb, PositiveReturnProb, BigGainProb),
nrow=1, # number of rows
ncol=4, # number of columns
byrow = TRUE)
dimnames(BasicStat) = list(
c("Probability"), # row names
c("BigLoss", "NegativeReturn", "PositiveReturn", "BigGain"))
show(BasicStat) BigLoss NegativeReturn PositiveReturn BigGain
Probability 0.06763926 0.4774536 0.5225464 0.05172414skewness(Asset$LogReturn) LogReturn
-0.1333265 kurtosis(Asset$LogReturn)LogReturn
6.240177 - 盒形圖
Asset$Price = Ad(APPLE)
Asset = na.omit(Asset)
colnames(Asset) = c("LogReturn","Price")
asset=data.frame(date=index(Asset), coredata(Asset))
#as.Date(asset$date,'%m/%d/%Y')
#format(as.Date(asset$date,'%m/%d/%Y'),'%Y')
asset$date=format(as.Date(asset$date,'%m/%d/%Y'),'%Y')
fig0_1 = ggplot(asset, aes(x=date,y=Price , color=date)) +
geom_boxplot(outlier.colour="black", outlier.shape=8,
outlier.size=2)+ ggtitle("盒型圖觀察 - Price and LogReturn")
fig0_2 = ggplot(asset, aes(x=date,y=LogReturn , color=date)) +
geom_boxplot(outlier.colour="red", outlier.shape=8,
outlier.size=2)
library(gridExtra)
grid.arrange(fig0_1,fig0_2,nrow=2,ncol=1)
資料配適
- fit normal density
fig1 = ggplot(Asset, aes(x=LogReturn)) +
geom_histogram(aes(y=..density..),
stat="bin",
bins=50,
col="blue",
fill="green",
alpha=0.2) +
stat_function(fun=dnorm,
args=list(mean=Asset_mean, sd=Asset_sd),
col="red")
fig1 
- fit kernel density
需要注意adjust 的敏感度問題，若是太小，則會太過敏感
fig2 = ggplot(Asset, aes(x=LogReturn)) +
geom_histogram(aes(y=..density..),
stat="bin",
bins=50,
col="blue",
fill="green",
alpha=0.2)+
geom_density(adjust=1, colour='red')
fig2
- fit NIG distribution The parameters of the normal-inverse Gaussian distribution are often used to construct a heaviness and skewness plot called the NIG-triangle.
library(rugarch)
spec = arfimaspec(mean.model=list(armaOrder=c(0,0), include.mean=FALSE),
distribution.model="nig")
Out = arfimafit(data=Asset$LogReturn, spec=spec)
sigma = Out@fit$coef[1]
skew = Out@fit$coef[2]
shape = Out@fit$coef[3]
x = Out@fit$residuals
y = ddist(distribution="nig", x,
sigma=sigma, skew=skew, shape=shape)
nig = data.frame(x=x, y=y)- density function of nig distribution and kernal on residual 在有母數與無母數情況下去配適資料型態，並且進行比較，須將include.mean=FALSE，把平移部分移除比較才算公平。
fig3 = ggplot(nig, aes(x=x)) +
geom_histogram(aes(y=..density..),
stat="bin",
bins=50,
col="blue",
fill="green",
alpha=0.2) +
geom_line(aes(x=x, y=y), data=nig, colour='red')+
geom_density(adjust=1, colour='blue')
fig3
模型配適
ARMA-gjrGARCH-in-mean在conditional 下的模型假設是 at | F t-1 ~ N(0,σt)。 為了建立合適的ARMA-gjrGARCH-in-mean模型，我先決定ARMA的order，再決定gjrGARCH-in-mean的order。
ARMA order決定
關於決定ARMA的order 我用的方法是先觀察ACF與PACF，視ACF為Cut off 和PACF為Tail off，進而決定ARMA (p , q) ，再進一步確定ARMA的標準化殘差是否通過Ljung- Box檢定，我以p-value > 0.05為標準，意味著不拒絕Ho，則視為殘差為White noice。最後決定ARMA(0,0)。
ACF, PACF 觀察
- ACF, PACF 觀察
ticker = "APPLE "
acf(as.numeric(Asset$LogReturn), main=paste0(ticker,"-return"))
pacf(as.numeric(Asset$LogReturn), main=paste0(ticker,"-return"))
ARMA(0,0)-fit
- ARMA(0,0)-fit
ARMA_p=0
ARMA_q=0
spec1 = arfimaspec(mean.model = list(armaOrder = c(ARMA_p,ARMA_q),
include.mean=TRUE,
arfima=FALSE,
external.regressors=NULL),
distribution.model = "norm")
model1_fit = arfimafit(spec=spec1, data=Asset$LogReturn)
model1_fit##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000653 0.000525 1.244 0.21351
## sigma 0.014404 0.000371 38.833 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000653 0.000517 1.2618 0.207
## sigma 0.014404 0.000797 18.0737 0.000
##
## LogLikelihood : 2127.291
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.6374
## Bayes -5.6251
## Shibata -5.6374
## Hannan-Quinn -5.6326
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3943 0.5301
## Lag[2*(p+q)+(p+q)-1][2] 1.1715 0.4458
## Lag[4*(p+q)+(p+q)-1][5] 2.7114 0.4623
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 9.182 2.444e-03
## Lag[2*(p+q)+(p+q)-1][2] 9.619 2.410e-03
## Lag[4*(p+q)+(p+q)-1][5] 20.119 1.798e-05
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 9.661 2 0.0079817
## ARCH Lag[5] 24.518 5 0.0001726
## ARCH Lag[10] 34.372 10 0.0001597
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.1587
## Individual Statistics:
## mu 0.187
## sigma 2.028
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.61 0.749 1.07
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.650512model1_resid = model1_fit@fit$residuals
acf(model1_resid, main="Series residual")
pacf(model1_resid, main="Series residual")
AutoARMA
結果也是一樣 - AutoARMA
autorfima_fit = autoarfima(data=Asset$LogReturn, ar.max=2, ma.max = 2,
criterion = "AIC", method = "full")
autorfima_fit## $fit
##
## *----------------------------------*
## * ARFIMA Model Fit *
## *----------------------------------*
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000653 0.000525 1.244 0.21351
## sigma 0.014404 0.000371 38.833 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000653 0.000517 1.2618 0.207
## sigma 0.014404 0.000797 18.0737 0.000
##
## LogLikelihood : 2127.291
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.6374
## Bayes -5.6251
## Shibata -5.6374
## Hannan-Quinn -5.6326
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3943 0.5301
## Lag[2*(p+q)+(p+q)-1][2] 1.1715 0.4458
## Lag[4*(p+q)+(p+q)-1][5] 2.7114 0.4623
##
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 9.182 2.444e-03
## Lag[2*(p+q)+(p+q)-1][2] 9.619 2.410e-03
## Lag[4*(p+q)+(p+q)-1][5] 20.119 1.798e-05
##
##
## ARCH LM Tests
## ------------------------------------
## Statistic DoF P-Value
## ARCH Lag[2] 9.661 2 0.0079817
## ARCH Lag[5] 24.518 5 0.0001726
## ARCH Lag[10] 34.372 10 0.0001597
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.1587
## Individual Statistics:
## mu 0.187
## sigma 2.028
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 0.61 0.749 1.07
## Individual Statistic: 0.35 0.47 0.75
##
##
## Elapsed time : 0.02398801
##
##
## $rank.matrix
## ar1 ar2 ma1 ma2 im arf AIC converged
## 1 0 0 0 0 1 0 -5.637376 1
## 2 0 0 0 1 0 0 -5.637272 1
## 3 0 1 0 0 0 0 -5.637179 1
## 4 0 0 0 1 1 0 -5.636892 1
## 5 0 1 0 0 1 0 -5.636778 1
## 6 0 0 1 0 0 0 -5.636010 1
## 7 1 0 0 0 0 0 -5.635953 1
## 8 0 0 1 0 1 0 -5.635296 1
## 9 1 0 0 0 1 0 -5.635244 1
## 10 1 0 0 1 0 0 -5.635218 1
## 11 1 1 0 0 0 0 -5.635213 1
## 12 0 0 1 1 0 0 -5.635146 1
## 13 0 1 1 0 0 0 -5.635129 1
## 14 1 1 1 1 0 0 -5.634915 1
## 15 1 0 0 1 1 0 -5.634726 1
## 16 1 1 0 0 1 0 -5.634695 1
## 17 0 0 1 1 1 0 -5.634652 1
## 18 0 1 1 0 1 0 -5.634611 1
## 19 1 1 1 1 1 0 -5.634396 1
## 20 1 1 1 0 0 0 -5.633762 1
## 21 0 1 0 1 0 0 -5.633716 1
## 22 1 0 1 0 0 0 -5.633587 1
## 23 1 1 1 0 1 0 -5.633450 1
## 24 0 1 0 1 1 0 -5.633136 1
## 25 1 0 1 1 1 0 -5.633098 1
## 26 0 1 1 1 0 0 -5.633082 1
## 27 1 1 0 1 0 0 -5.632908 1
## 28 1 0 1 0 1 0 -5.632786 1
## 29 1 0 1 1 0 0 -5.632736 1
## 30 0 1 1 1 1 0 -5.632456 1
## 31 1 1 0 1 1 0 -5.632294 1ARMA+gjrGARCH-in-mean order 決定
進一步決定ARMA-gjrGARCH-in-mean的order，我以ARMA(0, 0)為基礎再加上gjrGARCH(q, p) 的order，採用方法為窮舉法，gjrGARCH(1,0)-in-mean => gjrGARCH(0, 1)-in-mean =>gjrGARCH(1,1)-in-mean … 直到標準化殘差的平方通過Ljung- Box檢定，我以p-value > 0.05為標準，意味著不拒絕Ho，則視為殘差平方為White noice。最後決定使用通過Ljung- Box檢定的gjrGARCH(1,1)-in-mean。
ARMA(0,0)+gjrGARCH(1,0)-in-mean
- ARMA(0,0)+gjrGARCH(1,0)-in-mean
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 0
DataSize = length(Asset$LogReturn)
WindowSize = 251
OutSample = DataSize-WindowSize
spec2 = ugarchspec(mean.model=list(armaOrder=c(ARMA_p,ARMA_q), include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=NULL,
archex=FALSE),
variance.model=list(model="gjrGARCH", garchOrder=c(GARCH_q,GARCH_p)),
distribution.model="norm")
modelfit2 = ugarchfit(spec=spec2,
data=Asset$LogReturn,
out.sample=OutSample,
solver="hybrid",
solver.control=list(tol=1e-5, delta=1e-5, trace=1)
)##
## Iter: 1 fn: 934.7649 Pars: -0.0000868020 2.5476468262 0.0000002876 0.0485638329 0.1093479937
## Iter: 2 fn: 934.7649 Pars: -0.0000868020 2.5476468262 0.0000002876 0.0485638329 0.1093479937
## solnp--> Completed in 2 iterationsmodelfit2##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000087 0.000000 -4078.0288 0.00000
## archm 2.547647 0.001487 1713.3089 0.00000
## omega 0.000000 0.000001 0.5264 0.59861
## alpha1 0.048564 0.000012 4080.7204 0.00000
## gamma1 0.109348 0.000076 1438.4897 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000087 0.000838 -0.103578 0.91750
## archm 2.547647 291.111776 0.008751 0.99302
## omega 0.000000 0.111694 0.000003 1.00000
## alpha1 0.048564 3.540033 0.013718 0.98906
## gamma1 0.109348 14.519268 0.007531 0.99399
##
## LogLikelihood : -934.7649
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.4882
## Bayes 7.5584
## Shibata 7.4874
## Hannan-Quinn 7.5164
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.486 0.22277
## Lag[2*(p+q)+(p+q)-1][2] 2.548 0.18614
## Lag[4*(p+q)+(p+q)-1][5] 6.855 0.05622
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.001982 0.9645
## Lag[2*(p+q)+(p+q)-1][2] 0.121634 0.9047
## Lag[4*(p+q)+(p+q)-1][5] 0.213752 0.9915
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 0.2355 0.500 2.000 0.6275
## ARCH Lag[4] 0.2472 1.397 1.611 0.9461
## ARCH Lag[6] 0.2883 2.222 1.500 0.9909
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 32.9574
## Individual Statistics:
## mu 0.6189
## archm 0.9320
## omega 1.3160
## alpha1 0.9323
## gamma1 0.9322
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 10.1752 1.592e-20 ***
## Negative Sign Bias 0.1191 9.053e-01
## Positive Sign Bias 6.4416 6.169e-10 ***
## Joint Effect 108.6560 2.136e-23 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 4154 0
## 2 30 6302 0
## 3 40 8193 0
## 4 50 10036 0
##
##
## Elapsed time : 1.890425ARMA(0,0)+gjrGARCH(0,1)-in-mean
- ARMA(0,0)+gjrGARCH(0,1)-in-mean
ARMA_p = 0
ARMA_q = 0
GARCH_q = 0
GARCH_p = 1
spec3 = ugarchspec(mean.model=list(armaOrder=c(ARMA_p,ARMA_q), include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=NULL,
archex=FALSE),
variance.model=list(model="gjrGARCH", garchOrder=c(GARCH_q,GARCH_p)),
distribution.model="norm")
modelfit3 = ugarchfit(spec=spec3,
data=Asset$LogReturn,
out.sample=OutSample,
solver="hybrid",
solver.control=list(tol=1e-5, delta=1e-5, trace=1)
)##
## Iter: 1 fn: 19001.4771 Pars: 0.3754184637 -22.1323444474 0.0000002847 0.9000000000
## solnp--> Solution not reliable....Problem Inverting Hessian.
##
## Trying nlminb solver...## Warning in nlminb(start = pars, objective = fun, gradient = gr, hessian =
## hessian, : unrecognized control elements named 'tol', 'delta' ignored## 0: 12544.921: 0.00838343 -10.0000 2.84713e-07 0.900000
## 1: 12544.921: 0.00838343 -10.0000 2.84713e-07 0.900000
## 2: 12544.921: 0.00838343 -10.000 2.84713e-07 0.900000
## 3: 12544.921: 0.00838343 -10.000 2.84713e-07 0.900000
## 4: 12544.921: 0.00838343 -10.000 2.84713e-07 0.900000
## 5: 12544.921: 0.00838343 -10.000 2.84713e-07 0.900000
## 6: 12544.914: 0.00838343 -10.000 2.84713e-07 0.900000
## 7: 12544.874: 0.00838343 -10.000 2.84715e-07 0.900000
## 8: 12544.239: 0.00838343 -10.000 2.84741e-07 0.900000
## 9: 12537.200: 0.00838343 -10.000 2.85029e-07 0.900001
## 10: 12496.943: 0.00838343 -10.000 2.86711e-07 0.900001
## 11: 11922.413: 0.00838343 -10.000 3.13611e-07 0.900002
## 12: 10484.679: 0.00838343 -10.000 4.21213e-07 0.900007
## 13: 9797.1185: 0.00838343 -9.99999 5.19368e-07 0.900161
## 14: 9296.6541: 0.00838343 -9.99989 6.47548e-07 0.900798
## 15: 9016.1614: 0.00838343 -9.99972 7.85519e-07 0.901395
## 16: 8862.6098: 0.00838343 -9.99942 9.34390e-07 0.901901
## 17: 8791.7559: 0.00838343 -9.99890 1.07780e-06 0.902208
## 18: 8765.1078: 0.00838343 -9.99824 1.19933e-06 0.902196
## 19: 8757.4658: 0.00838343 -9.99753 1.28072e-06 0.901986
## 20: 8227.3429: 0.00838343 -9.67189 2.93974e-06 0.768208
## 21: 1166.7291: 0.00838343 -4.04391 4.62639e-06 1.00000
## 22: 268.52666: 0.00838343 1.55788 4.64035e-05 0.420141
## 23: -513.79463: 0.00838343 -0.550017 5.20777e-05 0.385603
## 24: -540.04432: 0.00833652 -0.909401 5.44676e-05 0.379770
## 25: -548.70738: 0.00826984 -0.954039 5.64938e-05 0.379357
## 26: -579.43872: 0.00800272 -0.954122 6.48253e-05 0.383099
## 27: -625.69370: 0.00739731 -0.764942 8.25481e-05 0.398279
## 28: -652.96274: 0.00670520 -0.503342 0.000102029 0.419727
## 29: -662.53208: 0.00613080 -0.346296 0.000118101 0.439254
## 30: -666.50339: 0.00569715 -0.291495 0.000130360 0.454960
## 31: -668.61301: 0.00532402 -0.289542 0.000141043 0.469102
## 32: -669.01245: 0.00515365 -0.304675 0.000145980 0.475774
## 33: -669.02669: 0.00512279 -0.309590 0.000146889 0.477019
## 34: -669.02676: 0.00512245 -0.310175 0.000146906 0.477051
## 35: -669.02677: 0.00512325 -0.310389 0.000146891 0.477040
## 36: -669.02680: 0.00512522 -0.310722 0.000146858 0.477024
## 37: -669.02685: 0.00512858 -0.311147 0.000146812 0.477024
## 38: -669.02698: 0.00513778 -0.312102 0.000146710 0.477085
## 39: -669.02733: 0.00515976 -0.314037 0.000146505 0.477337
## 40: -669.02825: 0.00521680 -0.318482 0.000146045 0.478179
## 41: -669.03069: 0.00536441 -0.329021 0.000144973 0.480673
## 42: -669.03736: 0.00576114 -0.355751 0.000142297 0.487912
## 43: -669.05553: 0.00683053 -0.425322 0.000135425 0.508329
## 44: -669.10447: 0.00838343 -0.522761 0.000126210 0.540165
## 45: -669.14555: 0.00838343 -0.514723 0.000127496 0.543888
## 46: -669.15760: 0.00838343 -0.505155 0.000127821 0.544974
## 47: -669.15772: 0.00838343 -0.504284 0.000127797 0.544928
## 48: -669.15772: 0.00838343 -0.504281 0.000127793 0.544921
## 49: -669.15772: 0.00838343 -0.504280 0.000127787 0.544920
## 50: -669.15772: 0.00838343 -0.504278 0.000127773 0.544934
## 51: -669.15773: 0.00838343 -0.504274 0.000127741 0.544991
## 52: -669.15774: 0.00838343 -0.504267 0.000127659 0.545187
## 53: -669.15778: 0.00838343 -0.504257 0.000127453 0.545764
## 54: -669.15787: 0.00838343 -0.504241 0.000126919 0.547404
## 55: -669.15812: 0.00838343 -0.504212 0.000125506 0.551988
## 56: -669.15883: 0.00838343 -0.504151 0.000121580 0.565150
## 57: -669.16097: 0.00838343 -0.503955 0.000109581 0.606141
## 58: -669.16502: 0.00838343 -0.503128 7.84991e-05 0.713714
## 59: -669.19198: 0.00838343 -0.500820 5.10688e-05 0.810774
## 60: -669.26346: 0.00838343 -0.500769 4.75339e-05 0.833701
## 61: -669.33385: 0.00838343 -0.500098 4.17763e-05 0.850144
## 62: -669.38382: 0.00838343 -0.501507 3.09555e-05 0.885820
## 63: -669.47209: 0.00838343 -0.495942 2.09473e-05 0.923929
## 64: -669.47280: 0.00838343 -0.496017 2.09808e-05 0.924055
## 65: -669.47347: 0.00838343 -0.496399 2.09252e-05 0.924010
## 66: -669.47467: 0.00838343 -0.496606 2.07902e-05 0.924700
## 67: -669.47712: 0.00838343 -0.497936 2.09620e-05 0.923783
## 68: -669.48078: 0.00838343 -0.500275 1.91634e-05 0.930062
## 69: -669.49021: 0.00838343 -0.508945 2.00271e-05 0.927271
## 70: -669.49076: 0.00838343 -0.509698 2.01232e-05 0.926439
## 71: -669.49124: 0.00838343 -0.508551 2.01143e-05 0.926678
## 72: -669.49124: 0.00838343 -0.508739 2.01008e-05 0.926729
## 73: -669.49124: 0.00838343 -0.508711 2.00980e-05 0.926738
## 74: -669.49124: 0.00838343 -0.508711 2.00980e-05 0.926737modelfit3##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(0,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.008383 0.009116 0.91960 0.35778
## archm -0.508711 0.547473 -0.92920 0.35279
## omega 0.000020 0.000024 0.85104 0.39475
## beta1 0.926737 0.085205 10.87658 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.008383 0.005106 1.6420 0.100592
## archm -0.508711 0.289994 -1.7542 0.079394
## omega 0.000020 0.000009 2.2193 0.026465
## beta1 0.926737 0.028561 32.4473 0.000000
##
## LogLikelihood : 669.4912
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.3027
## Bayes -5.2465
## Shibata -5.3032
## Hannan-Quinn -5.2801
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1161 0.7333
## Lag[2*(p+q)+(p+q)-1][2] 0.9825 0.5039
## Lag[4*(p+q)+(p+q)-1][5] 2.1100 0.5927
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 8.282 0.0040030
## Lag[2*(p+q)+(p+q)-1][2] 8.489 0.0048007
## Lag[4*(p+q)+(p+q)-1][5] 14.105 0.0007716
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 0.4058 0.500 2.000 0.52410
## ARCH Lag[4] 7.0277 1.397 1.611 0.02787
## ARCH Lag[6] 8.4014 2.222 1.500 0.03335
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.2265
## Individual Statistics:
## mu 0.3085
## archm 0.2471
## omega 0.4275
## beta1 0.4202
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.07 1.24 1.6
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.7665 0.44414
## Negative Sign Bias 2.2855 0.02313 **
## Positive Sign Bias 1.5304 0.12720
## Joint Effect 9.8955 0.01948 **
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 31.95 0.03168
## 2 30 32.86 0.28324
## 3 40 48.12 0.15006
## 4 50 63.54 0.07921
##
##
## Elapsed time : 0.737992ARMA(0,0)+gjrGARCH(1,1)-in-mean
- ARMA(0,0)+gjrGARCH(1,1)-in-mean
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
spec4 = ugarchspec(mean.model=list(armaOrder=c(ARMA_p,ARMA_q), include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=NULL,
archex=FALSE),
variance.model=list(model="gjrGARCH", garchOrder=c(GARCH_q,GARCH_p)),
distribution.model="norm")
modelfit4 = ugarchfit(spec=spec4,
data=Asset$LogReturn,
out.sample=OutSample,
solver="hybrid",
solver.control=list(tol=1e-5, delta=1e-5, trace=1)
)##
## Iter: 1 fn: -662.4556 Pars: -0.0090597226 0.5502650734 0.0000002847 0.0500000000 0.9000000000 0.0500000000
## solnp--> Solution not reliable....Problem Inverting Hessian.
##
## Trying nlminb solver...## Warning in nlminb(start = pars, objective = fun, gradient = gr, hessian =
## hessian, : unrecognized control elements named 'tol', 'delta' ignored## 0: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 1: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 2: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 3: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 4: -673.72725: -0.00838343 0.551103 2.22045e-16 0.0537270 0.912013 0.0574923
## 5: -674.67526: -0.00838343 0.549406 1.40083e-07 0.0429460 0.925681 0.0561916
## 6: -674.99071: -0.00838343 0.508970 2.22045e-16 0.0477351 0.929302 0.0440796
## 7: -675.03938: -0.00838342 0.497096 7.08535e-08 0.0441846 0.929241 0.0530650
## 8: -675.25044: -0.00838229 0.496438 1.21353e-07 0.0399625 0.934984 0.0524340
## 9: -675.28857: -0.00837973 0.497246 1.24483e-07 0.0391744 0.936620 0.0520915
## 10: -675.29661: -0.00837716 0.497669 1.07695e-07 0.0399100 0.936386 0.0517363
## 11: -675.30816: -0.00836936 0.498073 6.19201e-08 0.0421632 0.935014 0.0513819
## 12: -675.31340: -0.00836155 0.497586 2.86515e-08 0.0438767 0.933758 0.0514457
## 13: -675.31881: -0.00834703 0.496211 2.22045e-16 0.0454233 0.932290 0.0523261
## 14: -675.32457: -0.00833158 0.494605 2.22045e-16 0.0455065 0.931765 0.0535745
## 15: -675.34607: -0.00826980 0.488524 2.22045e-16 0.0457221 0.930432 0.0567471
## 16: -675.41509: -0.00802269 0.467641 3.07537e-09 0.0462425 0.926577 0.0660253
## 17: -675.53564: -0.00751194 0.429542 3.40936e-08 0.0457442 0.921306 0.0812704
## 18: -675.77549: -0.00636731 0.351027 1.51953e-07 0.0416466 0.913794 0.110451
## 19: -676.07946: -0.00472301 0.246203 4.05161e-07 0.0307679 0.909267 0.146562
## 20: -676.45394: -0.00384388 0.195074 6.16301e-07 0.0199541 0.914882 0.156044
## 21: -676.50115: -0.00232168 0.102173 8.70993e-07 0.00000 0.957483 0.0955617
## 22: -677.57001: -0.00189987 0.0788842 9.58631e-07 0.00000 0.942497 0.125383
## 23: -677.76638: -0.00170474 0.0681252 9.69788e-07 0.00000 0.944385 0.115737
## 24: -677.83581: -0.00111757 0.0452484 9.89719e-07 0.00000 0.946450 0.103707
## 25: -677.85525: -0.000806462 0.0214039 9.91528e-07 0.00000 0.944548 0.110687
## 26: -677.85699: -0.000805537 0.0216985 9.89667e-07 0.00000 0.945187 0.108915
## 27: -677.85723: -0.000775769 0.0198735 9.88778e-07 0.00000 0.945463 0.108236
## 28: -677.85725: -0.000765626 0.0191914 9.88592e-07 0.00000 0.945496 0.108196
## 29: -677.85726: -0.000760140 0.0188224 9.88526e-07 0.00000 0.945504 0.108201
## 30: -677.85729: -0.000752301 0.0182969 9.88472e-07 0.00000 0.945515 0.108212
## 31: -677.85737: -0.000739457 0.0174369 9.88477e-07 0.00000 0.945532 0.108231
## 32: -677.85757: -0.000719116 0.0160755 9.88730e-07 0.00000 0.945558 0.108262
## 33: -677.85812: -0.000686692 0.0139044 9.89784e-07 0.00000 0.945597 0.108312
## 34: -677.85953: -0.000635854 0.0105044 9.93151e-07 0.00000 0.945656 0.108384
## 35: -677.86321: -0.000557757 0.00528158 1.00298e-06 0.00000 0.945732 0.108501
## 36: -677.87278: -0.000441098 -0.00251587 1.03025e-06 0.00000 0.945811 0.108663
## 37: -677.89725: -0.000280928 -0.0132179 1.10314e-06 0.00000 0.945819 0.108882
## 38: -677.95917: -9.27129e-05 -0.0258089 1.29407e-06 0.00000 0.945527 0.109133
## 39: -678.10911: 3.12973e-05 -0.0342733 1.77541e-06 0.00000 0.944287 0.109380
## 40: -678.44014: -0.000190625 -0.0205534 2.91004e-06 0.00000 0.940526 0.109770
## 41: -678.86739: -0.000951733 0.0271388 4.44368e-06 0.00000 0.934498 0.110965
## 42: -679.71603: -0.00351712 0.186166 8.13389e-06 0.00000 0.918395 0.116008
## 43: -680.42737: -0.00744608 0.428583 1.31444e-05 0.00000 0.895304 0.123847
## 44: -680.73245: -0.00838343 0.491406 1.62264e-05 0.00000 0.884840 0.111601
## 45: -680.78082: -0.00838343 0.501440 1.66464e-05 0.00000 0.880966 0.112947
## 46: -680.81060: -0.00838343 0.508258 1.70575e-05 0.00000 0.875642 0.117548
## 47: -680.81411: -0.00838343 0.508131 1.71626e-05 0.00000 0.874178 0.118847
## 48: -680.81424: -0.00838343 0.508091 1.72228e-05 2.82041e-05 0.873300 0.119588
## 49: -680.82045: -0.00838343 0.505914 1.70660e-05 0.00245210 0.873166 0.116408
## 50: -680.82345: -0.00838343 0.503453 1.72494e-05 0.00467237 0.870477 0.116926
## 51: -680.82371: -0.00838303 0.503466 1.72609e-05 0.00476419 0.870489 0.116945
## 52: -680.82434: -0.00838264 0.503636 1.72344e-05 0.00500743 0.870350 0.116991
## 53: -680.82900: -0.00838343 0.503696 1.74217e-05 0.00773695 0.866771 0.117364
## 54: -680.83823: -0.00838343 0.503481 1.85763e-05 0.0161857 0.853621 0.119136
## 55: -680.84349: -0.00838343 0.505952 1.91589e-05 0.0181709 0.848895 0.120233
## 56: -680.84986: -0.00838343 0.508994 2.01803e-05 0.0186551 0.843488 0.122202
## 57: -680.85153: -0.00838343 0.508267 2.09402e-05 0.0191149 0.839434 0.123897
## 58: -680.85176: -0.00838343 0.507982 2.10188e-05 0.0178028 0.840113 0.124450
## 59: -680.85182: -0.00838343 0.507670 2.10860e-05 0.0182449 0.839358 0.124663
## 60: -680.85182: -0.00838343 0.507708 2.10706e-05 0.0182115 0.839440 0.124666
## 61: -680.85182: -0.00838343 0.507710 2.10695e-05 0.0181997 0.839446 0.124682
## 62: -680.85182: -0.00838343 0.507710 2.10698e-05 0.0181997 0.839444 0.124683modelfit4##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.008383 0.005463 -1.53464 0.124872
## archm 0.507710 0.354292 1.43303 0.151850
## omega 0.000021 0.000020 1.04747 0.294880
## alpha1 0.018200 0.055010 0.33085 0.740761
## beta1 0.839444 0.123700 6.78613 0.000000
## gamma1 0.124683 0.075334 1.65508 0.097909
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.008383 0.005546 -1.51169 0.130612
## archm 0.507710 0.353722 1.43534 0.151191
## omega 0.000021 0.000033 0.64120 0.521394
## alpha1 0.018200 0.072434 0.25126 0.801613
## beta1 0.839444 0.203718 4.12062 0.000038
## gamma1 0.124683 0.082347 1.51412 0.129994
##
## LogLikelihood : 680.8518
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.3773
## Bayes -5.2930
## Shibata -5.3784
## Hannan-Quinn -5.3434
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.06179 0.8037
## Lag[2*(p+q)+(p+q)-1][2] 0.85107 0.5492
## Lag[4*(p+q)+(p+q)-1][5] 1.47071 0.7471
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9968 0.3181
## Lag[2*(p+q)+(p+q)-1][5] 2.6722 0.4702
## Lag[4*(p+q)+(p+q)-1][9] 5.1836 0.4029
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.3864 0.500 2.000 0.5342
## ARCH Lag[5] 2.4569 1.440 1.667 0.3788
## ARCH Lag[7] 3.1620 2.315 1.543 0.4835
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.1318
## Individual Statistics:
## mu 0.22134
## archm 0.30601
## omega 0.08480
## alpha1 0.05103
## beta1 0.06404
## gamma1 0.07777
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5288 0.1276
## Negative Sign Bias 0.3088 0.7578
## Positive Sign Bias 0.9890 0.3237
## Joint Effect 3.8478 0.2784
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 21.27 0.3220
## 2 30 36.69 0.1543
## 3 40 46.85 0.1815
## 4 50 44.42 0.6591
##
##
## Elapsed time : 0.9813628以下公式是參考課本符號與假設所建立合適的ARMA(0,0)-gjrGARCH(1,1)-in-mean模型
\[\begin{align} Y_t - \mu_t &= a_t ,\\ a_t | F_{t-1} \sim \hbox{iid} \mathcal{N}(0, \sigma_{t}^2)\\ \mu_t &= -0.000086+ 0.507712 * \sigma_{t}^2 , \\ \sigma_{t}^2 &= 0.000021 + 0.018202 a_{t-1}^2 + 0.839439 \sigma_{t-1}^2 + 0.124684 I(a_{t-1}<0) a_{t-1}^2 .\\ \end{align}\]預測
ARMA(0,0)+gjrGARCH(1,1)
固定參數下預測
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
spec4 = ugarchspec(mean.model=list(armaOrder=c(ARMA_p,ARMA_q), include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=NULL,
archex=FALSE),
variance.model=list(model="gjrGARCH", garchOrder=c(GARCH_q,GARCH_p)),
distribution.model="norm")
modelfit4 = ugarchfit(spec=spec4,
data=Asset$LogReturn,
out.sample=OutSample,
solver="hybrid",
solver.control=list(tol=1e-5, delta=1e-5, trace=1)
)##
## Iter: 1 fn: -662.4556 Pars: -0.0090597226 0.5502650734 0.0000002847 0.0500000000 0.9000000000 0.0500000000
## solnp--> Solution not reliable....Problem Inverting Hessian.
##
## Trying nlminb solver...## Warning in nlminb(start = pars, objective = fun, gradient = gr, hessian =
## hessian, : unrecognized control elements named 'tol', 'delta' ignored## 0: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 1: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 2: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 3: -664.67913: -0.00838343 0.550265 2.84713e-07 0.0500000 0.900000 0.0500000
## 4: -673.72725: -0.00838343 0.551103 2.22045e-16 0.0537270 0.912013 0.0574923
## 5: -674.67526: -0.00838343 0.549406 1.40083e-07 0.0429460 0.925681 0.0561916
## 6: -674.99071: -0.00838343 0.508970 2.22045e-16 0.0477351 0.929302 0.0440796
## 7: -675.03938: -0.00838342 0.497096 7.08535e-08 0.0441846 0.929241 0.0530650
## 8: -675.25044: -0.00838229 0.496438 1.21353e-07 0.0399625 0.934984 0.0524340
## 9: -675.28857: -0.00837973 0.497246 1.24483e-07 0.0391744 0.936620 0.0520915
## 10: -675.29661: -0.00837716 0.497669 1.07695e-07 0.0399100 0.936386 0.0517363
## 11: -675.30816: -0.00836936 0.498073 6.19201e-08 0.0421632 0.935014 0.0513819
## 12: -675.31340: -0.00836155 0.497586 2.86515e-08 0.0438767 0.933758 0.0514457
## 13: -675.31881: -0.00834703 0.496211 2.22045e-16 0.0454233 0.932290 0.0523261
## 14: -675.32457: -0.00833158 0.494605 2.22045e-16 0.0455065 0.931765 0.0535745
## 15: -675.34607: -0.00826980 0.488524 2.22045e-16 0.0457221 0.930432 0.0567471
## 16: -675.41509: -0.00802269 0.467641 3.07537e-09 0.0462425 0.926577 0.0660253
## 17: -675.53564: -0.00751194 0.429542 3.40936e-08 0.0457442 0.921306 0.0812704
## 18: -675.77549: -0.00636731 0.351027 1.51953e-07 0.0416466 0.913794 0.110451
## 19: -676.07946: -0.00472301 0.246203 4.05161e-07 0.0307679 0.909267 0.146562
## 20: -676.45394: -0.00384388 0.195074 6.16301e-07 0.0199541 0.914882 0.156044
## 21: -676.50115: -0.00232168 0.102173 8.70993e-07 0.00000 0.957483 0.0955617
## 22: -677.57001: -0.00189987 0.0788842 9.58631e-07 0.00000 0.942497 0.125383
## 23: -677.76638: -0.00170474 0.0681252 9.69788e-07 0.00000 0.944385 0.115737
## 24: -677.83581: -0.00111757 0.0452484 9.89719e-07 0.00000 0.946450 0.103707
## 25: -677.85525: -0.000806462 0.0214039 9.91528e-07 0.00000 0.944548 0.110687
## 26: -677.85699: -0.000805537 0.0216985 9.89667e-07 0.00000 0.945187 0.108915
## 27: -677.85723: -0.000775769 0.0198735 9.88778e-07 0.00000 0.945463 0.108236
## 28: -677.85725: -0.000765626 0.0191914 9.88592e-07 0.00000 0.945496 0.108196
## 29: -677.85726: -0.000760140 0.0188224 9.88526e-07 0.00000 0.945504 0.108201
## 30: -677.85729: -0.000752301 0.0182969 9.88472e-07 0.00000 0.945515 0.108212
## 31: -677.85737: -0.000739457 0.0174369 9.88477e-07 0.00000 0.945532 0.108231
## 32: -677.85757: -0.000719116 0.0160755 9.88730e-07 0.00000 0.945558 0.108262
## 33: -677.85812: -0.000686692 0.0139044 9.89784e-07 0.00000 0.945597 0.108312
## 34: -677.85953: -0.000635854 0.0105044 9.93151e-07 0.00000 0.945656 0.108384
## 35: -677.86321: -0.000557757 0.00528158 1.00298e-06 0.00000 0.945732 0.108501
## 36: -677.87278: -0.000441098 -0.00251587 1.03025e-06 0.00000 0.945811 0.108663
## 37: -677.89725: -0.000280928 -0.0132179 1.10314e-06 0.00000 0.945819 0.108882
## 38: -677.95917: -9.27129e-05 -0.0258089 1.29407e-06 0.00000 0.945527 0.109133
## 39: -678.10911: 3.12973e-05 -0.0342733 1.77541e-06 0.00000 0.944287 0.109380
## 40: -678.44014: -0.000190625 -0.0205534 2.91004e-06 0.00000 0.940526 0.109770
## 41: -678.86739: -0.000951733 0.0271388 4.44368e-06 0.00000 0.934498 0.110965
## 42: -679.71603: -0.00351712 0.186166 8.13389e-06 0.00000 0.918395 0.116008
## 43: -680.42737: -0.00744608 0.428583 1.31444e-05 0.00000 0.895304 0.123847
## 44: -680.73245: -0.00838343 0.491406 1.62264e-05 0.00000 0.884840 0.111601
## 45: -680.78082: -0.00838343 0.501440 1.66464e-05 0.00000 0.880966 0.112947
## 46: -680.81060: -0.00838343 0.508258 1.70575e-05 0.00000 0.875642 0.117548
## 47: -680.81411: -0.00838343 0.508131 1.71626e-05 0.00000 0.874178 0.118847
## 48: -680.81424: -0.00838343 0.508091 1.72228e-05 2.82041e-05 0.873300 0.119588
## 49: -680.82045: -0.00838343 0.505914 1.70660e-05 0.00245210 0.873166 0.116408
## 50: -680.82345: -0.00838343 0.503453 1.72494e-05 0.00467237 0.870477 0.116926
## 51: -680.82371: -0.00838303 0.503466 1.72609e-05 0.00476419 0.870489 0.116945
## 52: -680.82434: -0.00838264 0.503636 1.72344e-05 0.00500743 0.870350 0.116991
## 53: -680.82900: -0.00838343 0.503696 1.74217e-05 0.00773695 0.866771 0.117364
## 54: -680.83823: -0.00838343 0.503481 1.85763e-05 0.0161857 0.853621 0.119136
## 55: -680.84349: -0.00838343 0.505952 1.91589e-05 0.0181709 0.848895 0.120233
## 56: -680.84986: -0.00838343 0.508994 2.01803e-05 0.0186551 0.843488 0.122202
## 57: -680.85153: -0.00838343 0.508267 2.09402e-05 0.0191149 0.839434 0.123897
## 58: -680.85176: -0.00838343 0.507982 2.10188e-05 0.0178028 0.840113 0.124450
## 59: -680.85182: -0.00838343 0.507670 2.10860e-05 0.0182449 0.839358 0.124663
## 60: -680.85182: -0.00838343 0.507708 2.10706e-05 0.0182115 0.839440 0.124666
## 61: -680.85182: -0.00838343 0.507710 2.10695e-05 0.0181997 0.839446 0.124682
## 62: -680.85182: -0.00838343 0.507710 2.10698e-05 0.0181997 0.839444 0.124683modelfit4##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.008383 0.005463 -1.53464 0.124872
## archm 0.507710 0.354292 1.43303 0.151850
## omega 0.000021 0.000020 1.04747 0.294880
## alpha1 0.018200 0.055010 0.33085 0.740761
## beta1 0.839444 0.123700 6.78613 0.000000
## gamma1 0.124683 0.075334 1.65508 0.097909
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.008383 0.005546 -1.51169 0.130612
## archm 0.507710 0.353722 1.43534 0.151191
## omega 0.000021 0.000033 0.64120 0.521394
## alpha1 0.018200 0.072434 0.25126 0.801613
## beta1 0.839444 0.203718 4.12062 0.000038
## gamma1 0.124683 0.082347 1.51412 0.129994
##
## LogLikelihood : 680.8518
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.3773
## Bayes -5.2930
## Shibata -5.3784
## Hannan-Quinn -5.3434
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.06179 0.8037
## Lag[2*(p+q)+(p+q)-1][2] 0.85107 0.5492
## Lag[4*(p+q)+(p+q)-1][5] 1.47071 0.7471
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9968 0.3181
## Lag[2*(p+q)+(p+q)-1][5] 2.6722 0.4702
## Lag[4*(p+q)+(p+q)-1][9] 5.1836 0.4029
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.3864 0.500 2.000 0.5342
## ARCH Lag[5] 2.4569 1.440 1.667 0.3788
## ARCH Lag[7] 3.1620 2.315 1.543 0.4835
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.1318
## Individual Statistics:
## mu 0.22134
## archm 0.30601
## omega 0.08480
## alpha1 0.05103
## beta1 0.06404
## gamma1 0.07777
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.49 1.68 2.12
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.5288 0.1276
## Negative Sign Bias 0.3088 0.7578
## Positive Sign Bias 0.9890 0.3237
## Joint Effect 3.8478 0.2784
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 21.27 0.3220
## 2 30 36.69 0.1543
## 3 40 46.85 0.1815
## 4 50 44.42 0.6591
##
##
## Elapsed time : 0.9338319spec4 = getspec(modelfit4)
setfixed(spec4)= as.list(coef(modelfit4))
forecast4 = ugarchforecast(spec4,
data = Asset$LogReturn,
n.ahead = 1,
n.roll = OutSample-1,
out.sample = OutSample)plot(forecast4, which=2)
return_forecast4=forecast4@forecast$seriesFor
return_forecast4_1=forecast4@forecast$sigmaFor
length(fitted(forecast4))## [1] 503Asset$Returnforecast = NA
Asset$Sigmaforecast = NA
Asset$Returnforecast[(DataSize-OutSample+1):DataSize] = return_forecast4[1:OutSample]
Asset$Sigmaforecast[(DataSize-OutSample+1):DataSize] = return_forecast4_1[1:OutSample]
plot(index(Asset),Asset$LogReturn, type='l', col ='blue', lty=1, xlab='time', ylab='daily return')
lines(index(Asset), Asset$Returnforecast, type='l', col='red', lty=2)
lines(index(Asset), Asset$Sigmaforecast, type='l', col='green', lty=2)
解釋變數置入模型
簡單回歸分析 - 檢查線性性
解釋變數在VIF>10以上，事先排除掉，避免多元共線性問題
library(car)
library(MASS)
start = "2015-01-01"
end = "2017-12-31"
APPLE = getSymbols("AAPL",from=start,to=end, src = "yahoo", auto.assign = FALSE )
FB = getSymbols("FB",from=start,to=end, src = "yahoo", auto.assign = FALSE )
AMAZON = getSymbols("AMZN",from=start,to=end, src = "yahoo", auto.assign = FALSE )
GOOGLE = getSymbols("GOOGL",from=start,to=end, src = "yahoo", auto.assign = FALSE )
APPLE$APPLreturn = TTR::ROC(Ad(APPLE),type="continuous")
FB$FBreturn = TTR::ROC(Ad(FB),type="continuous")
AMAZON$AMZNreturn = TTR::ROC(Ad(AMAZON),type="continuous")
GOOGLE$GOOGLreturn = TTR::ROC(Ad(GOOGLE),type="continuous")
Return = cbind(APPLE$APPLreturn,FB$FBreturn,AMAZON$AMZNreturn,GOOGLE$GOOGLreturn)
Return = na.omit(Return)
pairs(APPLreturn ~ FBreturn + AMZNreturn + GOOGLreturn, data=Return)
out=lm(APPLreturn ~ FBreturn + AMZNreturn + GOOGLreturn, data=Return)
summary(out)##
## Call:
## lm(formula = APPLreturn ~ FBreturn + AMZNreturn + GOOGLreturn,
## data = Return)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.062407 -0.005684 0.000093 0.006668 0.057268
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.313e-05 4.541e-04 0.029 0.97693
## FBreturn 2.844e-01 4.006e-02 7.098 2.93e-12 ***
## AMZNreturn 9.278e-02 3.384e-02 2.742 0.00625 **
## GOOGLreturn 1.856e-01 4.568e-02 4.064 5.34e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01241 on 750 degrees of freedom
## Multiple R-squared: 0.2622, Adjusted R-squared: 0.2592
## F-statistic: 88.83 on 3 and 750 DF, p-value: < 2.2e-16vif(out) ## FBreturn AMZNreturn GOOGLreturn
## 1.791543 1.759202 1.935804Regressor.mean = as.matrix(cbind(Return$FBreturn,Return$AMZNreturn,Return$GOOGLreturn))
Regressor.variance = as.matrix(cbind((Return$FBreturn)^2,(Return$AMZNreturn)^2,(Return$GOOGLreturn)^2))模型配合
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
spec5 = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=Regressor.mean,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p),
submodel=NULL,
external.regressors=Regressor.variance,
variance.targeting=FALSE),
distribution.model="norm")
modelfit5 = ugarchfit(spec=spec5, data=Return$APPLreturn, solver="hybrid")
modelfit5##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000775 0.001227 0.631642 0.527621
## archm -0.078005 0.116216 -0.671213 0.502085
## mxreg1 0.343270 0.040556 8.464008 0.000000
## mxreg2 0.112025 0.031812 3.521434 0.000429
## mxreg3 0.154276 0.046597 3.310850 0.000930
## omega 0.000008 0.000000 49.415941 0.000000
## alpha1 0.003867 0.016628 0.232568 0.816097
## beta1 0.838383 0.019628 42.713723 0.000000
## gamma1 0.232062 0.049212 4.715609 0.000002
## vxreg1 0.000000 0.006315 0.000002 0.999999
## vxreg2 0.000000 0.001945 0.000005 0.999996
## vxreg3 0.000000 0.002517 0.000004 0.999997
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000775 0.002126 0.364591 0.715417
## archm -0.078005 0.182701 -0.426957 0.669411
## mxreg1 0.343270 0.073459 4.672950 0.000003
## mxreg2 0.112025 0.033695 3.324648 0.000885
## mxreg3 0.154276 0.075885 2.033012 0.042051
## omega 0.000008 0.000000 37.926100 0.000000
## alpha1 0.003867 0.035437 0.109126 0.913103
## beta1 0.838383 0.040477 20.712822 0.000000
## gamma1 0.232062 0.072273 3.210925 0.001323
## vxreg1 0.000000 0.008143 0.000001 0.999999
## vxreg2 0.000000 0.001964 0.000005 0.999996
## vxreg3 0.000000 0.002754 0.000004 0.999997
##
## LogLikelihood : 2299.802
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.0684
## Bayes -5.9948
## Shibata -6.0689
## Hannan-Quinn -6.0401
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.122 0.2895
## Lag[2*(p+q)+(p+q)-1][2] 2.184 0.2340
## Lag[4*(p+q)+(p+q)-1][5] 3.214 0.3694
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.004709 0.9453
## Lag[2*(p+q)+(p+q)-1][5] 0.336814 0.9797
## Lag[4*(p+q)+(p+q)-1][9] 0.758346 0.9941
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.05638 0.500 2.000 0.8123
## ARCH Lag[5] 0.71949 1.440 1.667 0.8175
## ARCH Lag[7] 0.85763 2.315 1.543 0.9356
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 18.2369
## Individual Statistics:
## mu 0.07673
## archm 0.06505
## mxreg1 0.10144
## mxreg2 0.26893
## mxreg3 0.21054
## omega 1.04965
## alpha1 0.46794
## beta1 0.17509
## gamma1 0.14785
## vxreg1 1.15077
## vxreg2 1.79842
## vxreg3 1.99042
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.69 2.96 3.51
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.8698 0.0619 *
## Negative Sign Bias 0.4644 0.6425
## Positive Sign Bias 0.8231 0.4107
## Joint Effect 3.8588 0.2771
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 53.27 4.265e-05
## 2 30 67.22 7.208e-05
## 3 40 87.49 1.394e-05
## 4 50 88.97 4.169e-04
##
##
## Elapsed time : 1.307266精簡模型1
直接篩選掉不顯著的係數且滿足殘差通過，決定最後有解釋變數模型。
ARMA_p = 0
ARMA_q = 0
GARCH_q = 0
GARCH_p = 1
spec6 = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=Regressor.mean,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="norm")
modelfit6 = ugarchfit(spec=spec6, data=Return$APPLreturn, solver="hybrid")
modelfit6##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(0,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.009212 0.000038 244.2915 0.00000
## archm -0.784573 0.039477 -19.8741 0.00000
## mxreg1 0.253354 0.040587 6.2422 0.00000
## mxreg2 0.114787 0.034129 3.3633 0.00077
## mxreg3 0.206939 0.046809 4.4209 0.00001
## omega 0.000000 0.000000 0.0000 1.00000
## beta1 0.998570 0.000004 226965.1251 0.00000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.009212 0.000227 40.6132 0.000000
## archm -0.784573 0.210598 -3.7255 0.000195
## mxreg1 0.253354 0.074152 3.4167 0.000634
## mxreg2 0.114787 0.036315 3.1609 0.001573
## mxreg3 0.206939 0.085234 2.4279 0.015187
## omega 0.000000 0.000007 0.0000 1.000000
## beta1 0.998570 0.000010 102648.5896 0.000000
##
## LogLikelihood : 2268.291
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.9981
## Bayes -5.9552
## Shibata -5.9983
## Hannan-Quinn -5.9816
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.793 0.09465
## Lag[2*(p+q)+(p+q)-1][2] 3.360 0.11217
## Lag[4*(p+q)+(p+q)-1][5] 4.792 0.17047
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 19.72 8.969e-06
## Lag[2*(p+q)+(p+q)-1][2] 20.58 3.135e-06
## Lag[4*(p+q)+(p+q)-1][5] 24.22 1.318e-06
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 1.712 0.500 2.000 0.19078
## ARCH Lag[4] 5.424 1.397 1.611 0.06939
## ARCH Lag[6] 6.763 2.222 1.500 0.07980
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 160.4905
## Individual Statistics:
## mu 0.4996
## archm 0.4020
## mxreg1 0.1183
## mxreg2 0.1947
## mxreg3 0.1165
## omega 83.8032
## beta1 0.2068
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.353 1.766e-01
## Negative Sign Bias 4.342 1.604e-05 ***
## Positive Sign Bias 1.149 2.508e-01
## Joint Effect 20.215 1.532e-04 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 54.75 2.535e-05
## 2 30 73.51 9.898e-06
## 3 40 86.00 2.159e-05
## 4 50 104.49 6.804e-06
##
##
## Elapsed time : 1.24508精簡模型2
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 0
spec7 = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=Regressor.mean,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="norm")
modelfit7 = ugarchfit(spec=spec7, data=Return$APPLreturn, solver="hybrid")
modelfit7##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,0)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.002263 0.004989 -0.45349 0.650192
## archm 0.186594 0.419713 0.44457 0.656627
## mxreg1 0.287826 0.042727 6.73638 0.000000
## mxreg2 0.123063 0.033282 3.69761 0.000218
## mxreg3 0.177334 0.045968 3.85779 0.000114
## omega 0.000123 0.000008 15.79086 0.000000
## alpha1 0.119321 0.053218 2.24209 0.024955
## gamma1 0.138270 0.097618 1.41645 0.156645
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.002263 0.008323 -0.27184 0.785744
## archm 0.186594 0.708028 0.26354 0.792134
## mxreg1 0.287826 0.069404 4.14710 0.000034
## mxreg2 0.123063 0.036888 3.33612 0.000850
## mxreg3 0.177334 0.088244 2.00959 0.044475
## omega 0.000123 0.000017 7.30761 0.000000
## alpha1 0.119321 0.095339 1.25155 0.210734
## gamma1 0.138270 0.157933 0.87550 0.381302
##
## LogLikelihood : 2264.281
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.9848
## Bayes -5.9358
## Shibata -5.9851
## Hannan-Quinn -5.9659
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.9516 0.3293
## Lag[2*(p+q)+(p+q)-1][2] 1.8458 0.2897
## Lag[4*(p+q)+(p+q)-1][5] 3.2864 0.3572
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.0452 0.8316
## Lag[2*(p+q)+(p+q)-1][2] 0.5772 0.6585
## Lag[4*(p+q)+(p+q)-1][5] 3.0098 0.4053
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 1.058 0.500 2.000 0.3036
## ARCH Lag[4] 3.579 1.397 1.611 0.1925
## ARCH Lag[6] 4.447 2.222 1.500 0.2510
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.7841
## Individual Statistics:
## mu 0.2523
## archm 0.2163
## mxreg1 0.1456
## mxreg2 0.1632
## mxreg3 0.1133
## omega 1.2266
## alpha1 0.3863
## gamma1 0.4225
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.89 2.11 2.59
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.0362 0.04208 **
## Negative Sign Bias 0.8656 0.38698
## Positive Sign Bias 1.0273 0.30462
## Joint Effect 4.1661 0.24408
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 70.30 8.209e-08
## 2 30 75.10 5.899e-06
## 3 40 87.27 1.485e-05
## 4 50 93.88 1.205e-04
##
##
## Elapsed time : 3.810701精簡模型3
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
spec8 = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
external.regressors=Regressor.mean,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="norm")
modelfit8 = ugarchfit(spec=spec8, data=Return$APPLreturn, solver="hybrid")
modelfit8##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000793 0.000905 0.87703 0.380472
## archm -0.079642 0.087669 -0.90844 0.363646
## mxreg1 0.343292 0.039181 8.76173 0.000000
## mxreg2 0.112022 0.031054 3.60736 0.000309
## mxreg3 0.154187 0.042056 3.66622 0.000246
## omega 0.000008 0.000000 33.97550 0.000000
## alpha1 0.003820 0.015767 0.24229 0.808554
## beta1 0.838657 0.018159 46.18335 0.000000
## gamma1 0.231650 0.047784 4.84788 0.000001
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000793 0.001960 0.40479 0.685635
## archm -0.079642 0.164606 -0.48384 0.628502
## mxreg1 0.343292 0.069133 4.96569 0.000001
## mxreg2 0.112022 0.034761 3.22261 0.001270
## mxreg3 0.154187 0.072678 2.12149 0.033880
## omega 0.000008 0.000000 37.51318 0.000000
## alpha1 0.003820 0.034597 0.11042 0.912075
## beta1 0.838657 0.040654 20.62906 0.000000
## gamma1 0.231650 0.066975 3.45877 0.000543
##
## LogLikelihood : 2299.802
##
## Information Criteria
## ------------------------------------
##
## Akaike -6.0764
## Bayes -6.0212
## Shibata -6.0767
## Hannan-Quinn -6.0551
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.118 0.2903
## Lag[2*(p+q)+(p+q)-1][2] 2.183 0.2341
## Lag[4*(p+q)+(p+q)-1][5] 3.217 0.3688
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.005044 0.9434
## Lag[2*(p+q)+(p+q)-1][5] 0.338241 0.9795
## Lag[4*(p+q)+(p+q)-1][9] 0.759754 0.9941
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.05658 0.500 2.000 0.8120
## ARCH Lag[5] 0.72029 1.440 1.667 0.8173
## ARCH Lag[7] 0.85822 2.315 1.543 0.9355
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 10.1146
## Individual Statistics:
## mu 0.07648
## archm 0.06498
## mxreg1 0.10134
## mxreg2 0.26864
## mxreg3 0.20998
## omega 1.04583
## alpha1 0.46933
## beta1 0.17568
## gamma1 0.14929
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.1 2.32 2.82
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.8698 0.0619 *
## Negative Sign Bias 0.4676 0.6402
## Positive Sign Bias 0.8216 0.4116
## Joint Effect 3.8554 0.2775
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 52.90 4.852e-05
## 2 30 65.71 1.144e-04
## 3 40 88.12 1.154e-05
## 4 50 88.97 4.169e-04
##
##
## Elapsed time : 1.400418滾動式分析
重新跑一次需要花很多時間，暫時拿掉
DataSize = length(Return$APPLreturn)
WindowSize = 252
OutSample = DataSize - WindowSize
#rolling = ugarchroll(spec=spec8,
# data=Return$APPLreturn,
# n.ahead=1,
# forecast.length=OutSample,
# refit.every=1,
# refit.window="moving",
# solver="hybrid",
# solver.control=list(tol=1e-5,delta=1e-5,trace=1),
# calculate.VaR = TRUE,
# VaR.alpha = c(0.01,0.05),
# parallel=TRUE,
# parallel.control = list(pkg=c("snowfall"), cores=4),
# keep.coef=TRUE)
#rolling = resume(rolling, solver="gosolnp")
#convergence(rolling)儲存與載入資料
#getwd()
#setwd("c:/temp")
#save(rolling, file="c:/temp/rolling.RData")
load("c:/temp/rolling.RData")
#rolling
#show(rolling)
#str(rolling)滾動式模型
rolling@model$coef[[1]]$index[1] “2016-01-04”
#rolling@forecast$VaR[[1]]
#rolling@forecast$density$Mu
str(rolling@forecast$density)‘data.frame’: 502 obs. of 6 variables: $ Mu : num 0.00142 0.00056 -0.02614 -0.00395 0.00143 … $ Sigma : num 0.0138 0.0154 0.0161 0.0162 0.0159 … $ Skew : num 0 0 0 0 0 0 0 0 0 0 … $ Shape : num 0 0 0 0 0 0 0 0 0 0 … $ Shape(GIG): num 0 0 0 0 0 0 0 0 0 0 … $ Realized : num -0.02538 -0.01976 -0.04312 0.00527 0.01606 …
#rolling@model$coef[1]
rolling@model$coef[[1]]$coef[2,1][1] 0.5324135
rolling@model$coef[[1]]$coef[3,4][1] 3.219818e-07
rolling@model$coef[250][[1]][[1]]$index [1] “2016-12-28”
[[1]]$coef Estimate Std. Error t value Pr(>|t|) mu 3.177655e-03 0.04250773 7.475475e-02 0.9404098 archm -1.533683e-01 6.42076127 -2.388631e-02 0.9809433 mxreg1 1.442162e-01 2.77923359 5.189063e-02 0.9586158 mxreg2 5.793940e-02 20.98798608 2.760598e-03 0.9977974 mxreg3 4.293880e-01 41.81835705 1.026793e-02 0.9918075 omega 1.418424e-07 0.02002261 7.084113e-06 0.9999943 alpha1 1.706889e-02 35.16338207 4.854167e-04 0.9996127 beta1 8.458938e-01 82.70012929 1.022845e-02 0.9918390 gamma1 2.703380e-01 14.99862768 1.802418e-02 0.9856196
滾動式預測
#rolling@model$coef[[1]]$index
#rolling@forecast$VaR[[1]]
#rolling@forecast$density$Mu
str(rolling@forecast$density)‘data.frame’: 502 obs. of 6 variables: $ Mu : num 0.00142 0.00056 -0.02614 -0.00395 0.00143 … $ Sigma : num 0.0138 0.0154 0.0161 0.0162 0.0159 … $ Skew : num 0 0 0 0 0 0 0 0 0 0 … $ Shape : num 0 0 0 0 0 0 0 0 0 0 … $ Shape(GIG): num 0 0 0 0 0 0 0 0 0 0 … $ Realized : num -0.02538 -0.01976 -0.04312 0.00527 0.01606 …
rolling@model$coef[1][[1]][[1]]$index [1] “2016-01-04”
[[1]]$coef Estimate Std. Error t value Pr(>|t|) mu -8.011085e-03 6.385128e-03 -1.2546474 2.096068e-01 archm 5.324135e-01 4.807172e-01 1.1075400 2.680605e-01 mxreg1 4.577881e-01 8.958489e-02 5.1101038 3.219818e-07 mxreg2 6.797538e-02 4.381755e-02 1.5513275 1.208232e-01 mxreg3 5.008960e-02 9.852529e-02 0.5083933 6.111776e-01 omega 3.216611e-06 3.500082e-07 9.1901012 0.000000e+00 alpha1 0.000000e+00 1.047890e-02 0.0000000 1.000000e+00 beta1 9.553805e-01 1.332817e-02 71.6813118 0.000000e+00 gamma1 4.766936e-02 3.703671e-02 1.2870841 1.980650e-01
rolling@model$coef[[1]]$coef[2,1][1] 0.5324135
rolling@model$coef[[1]]$coef[3,4][1] 3.219818e-07
Return_1 = Return
Return_1$criteria = NA
Return_1$criteria = 0.05
n=DataSize+1-WindowSize
rolling@model$coef[[n-1]]$index[1] “2017-12-28”
Return_1$model_archm = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_archm[i] = rolling@model$coef[[i+1-WindowSize]]$coef[2,1]
}
Return_1$model_archm_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_archm_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[2,4]
}
Return_1$model_mxreg1 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg1[i] = rolling@model$coef[[i+1-WindowSize]]$coef[3,1]
}
Return_1$model_mxreg1_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg1_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[3,4]
}
Return_1$model_mxreg2 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg2[i] = rolling@model$coef[[i+1-WindowSize]]$coef[4,1]
}
Return_1$model_mxreg2_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg2_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[4,4]
}
Return_1$model_mxreg3 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg3[i] = rolling@model$coef[[i+1-WindowSize]]$coef[5,1]
}
Return_1$model_mxreg3_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_mxreg3_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[5,4]
}
Return_1$model_omega = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_omega[i] = rolling@model$coef[[i+1-WindowSize]]$coef[6,1]
}
Return_1$model_omega_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_omega_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[6,4]
}
Return_1$model_alpha1 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_alpha1[i] = rolling@model$coef[[i+1-WindowSize]]$coef[7,1]
}
Return_1$model_alpha1_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_alpha1_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[7,4]
}
Return_1$model_beta1 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_beta1[i] = rolling@model$coef[[i+1-WindowSize]]$coef[8,1]
}
Return_1$model_beta1_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_beta1_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[8,4]
}
Return_1$model_gamma1 = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_gamma1[i] = rolling@model$coef[[i+1-WindowSize]]$coef[9,1]
}
Return_1$model_gamma1_pvalue = NA
for (i in WindowSize:(DataSize-1)){
Return_1$model_gamma1_pvalue[i] = rolling@model$coef[[i+1-WindowSize]]$coef[9,4]
}
Return_1$ForecastRealize[(WindowSize+1):DataSize]=rolling@forecast$density$Realized
Return_1$ForecastMu[(WindowSize+1):DataSize]=rolling@forecast$density$Mu
Return_1$ForecastSigma[(WindowSize+1):DataSize]=rolling@forecast$density$Sigma
#str(rolling@forecast)
Return_1$ForecastVaR_1[(WindowSize+1):DataSize]=rolling@forecast$VaR[[1]]
Return_1$ForecastVaR_2[(WindowSize+1):DataSize]=rolling@forecast$VaR[[2]]
Return_2 = data.frame(date = index(Return_1), coredata(Return_1))風險溢酬對APPLE報酬的影響 與 顯著性(rolling)
從「風險溢酬對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，從2016年初到2017年底的參數估計的p-value幾乎都是高於0.05，意味著風險溢酬對APPLE報酬率不顯著影響。由於第一筆估計參數是由前251筆資料估計出來的，我們將推論的時間往前推251天，從2015年初到2017年底對APPLE部分不存在顯著的風險溢酬影響。
plot1_1 = ggplot(Return_2, aes(x=date, y=model_archm)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("風險溢酬對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot1_2 = ggplot(Return_2, aes(x=date, y=model_archm_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot1_1,plot1_2,nrow=2,ncol=1)
FB報酬對APPLE報酬的影響 與 顯著性(rolling)
從「FB報酬對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，2016年初參數估計與2017年中參數估計的p-value小於0.05，意味著FB報酬對APPLE報酬有顯著性影響。由於第一筆估計參數是由前251筆資料估計出來的，我們將推論的時間往前推251天，2015年初到2016年初與2016年中到2017年底，FB報酬對APPLE報酬有顯著性影響。
plot2_1 = ggplot(Return_2, aes(x=date, y=model_mxreg1)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("FB報酬對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot2_2 = ggplot(Return_2, aes(x=date, y=model_mxreg1_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot2_1,plot2_2,nrow=2,ncol=1)
AMAZON報酬對APPLE報酬的影響 與 顯著性(rolling)
從「AMAZON報酬對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，2017年底參數估計的p-value小於0.05，意味著AMAZON報酬對APPLE報酬有顯著性影響。由於第一筆估計參數是由前251筆資料估計出來的，我們將推論的時間往前推251天，2016年底到2017年底，FB報酬對APPLE報酬有顯著性影響。
plot3_1 = ggplot(Return_2, aes(x=date, y=model_mxreg2)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("AMAZON報酬對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot3_2 = ggplot(Return_2, aes(x=date, y=model_mxreg2_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot3_1,plot3_2,nrow=2,ncol=1)
GOOGLE報酬對APPLE報酬的影響 與 顯著性(rolling)
從「GOOGLE報酬對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，2016年底到2017年初參數估計的p-value小於0.05，意味著GOOGLE報酬對APPLE報酬有顯著性影響。由於第一筆估計參數是由前251筆資料估計出來的，我們將推論的時間往前推251天，2015年底到2017年初，GOOGLE報酬對APPLE報酬有顯著性影響。
plot4_1 = ggplot(Return_2, aes(x=date, y=model_mxreg3)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("GOOGLE報酬對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot4_2 = ggplot(Return_2, aes(x=date, y=model_mxreg3_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot4_1,plot4_2,nrow=2,ncol=1)
Omega對APPLE報酬的影響 與 顯著性(rolling)
從「Omega對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，變異數的常數項係數不對APPLE報酬有顯著性的影響。
plot5_1 = ggplot(Return_2, aes(x=date, y=model_omega)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("Omega對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot5_2 = ggplot(Return_2, aes(x=date, y=model_omega_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot5_1,plot5_2,nrow=2,ncol=1)
alpha對APPLE報酬的影響 與 顯著性(rolling)
從「alpha對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，ARCH項係數不對APPLE報酬有顯著性的影響。
plot6_1 = ggplot(Return_2, aes(x=date, y=model_alpha1)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("alpha對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot6_2 = ggplot(Return_2, aes(x=date, y=model_alpha1_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot6_1,plot6_2,nrow=2,ncol=1)
beta對APPLE報酬的影響 與 顯著性(rolling)
從「beta對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，GARCH項係數對APPLE報酬有顯著性的影響。
plot7_1 = ggplot(Return_2, aes(x=date, y=model_beta1)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("beta對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot7_2 = ggplot(Return_2, aes(x=date, y=model_beta1_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot7_1,plot7_2,nrow=2,ncol=1)
gamma對APPLE報酬的影響 與 顯著性(rolling)
從「gamma對APPLE報酬的影響 與 顯著性(rolling)」圖可以觀察，從2016年底到2018年底，波動不對稱性對APPLE報酬有顯著性的影響。
plot8_1 = ggplot(Return_2, aes(x=date, y=model_gamma1)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+ ggtitle("gamma對APPLE報酬的影響 與 顯著性_rolling")+
theme_economist() + scale_colour_economist()
plot8_2 = ggplot(Return_2, aes(x=date, y=model_gamma1_pvalue)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=criteria),colour="red")+
theme_economist(stata=TRUE) + scale_colour_economist(stata=TRUE)
library(gridExtra)
grid.arrange(plot8_1,plot8_2,nrow=2,ncol=1)
APPLE報酬 與 ForecastMu, ForecastSigma 關係
library(ggplot2)
plot9 = ggplot(Return_2, aes(x=date, y=APPLreturn)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=ForecastMu),colour="blue")+
geom_line(aes(y=ForecastSigma),colour="red")+ ggtitle("APPLE報酬 與 ForecastMu, ForecastSigma 關係_rolling")
plot9
APPLE報酬 與 VaR(0.01) 關係
我在這裡判別VaR是否合宜的邏輯是比較不正確的，因為我只是順帶把VaR的功能展示出來，而正確的邏輯是應該確認風險管理的主題，進一步找出合適的模型，進而決定VaR。 而在不同情境下VaR的應用是有所不同的，如果是以銀行的資本計提為主，這個模型太過敏感，並不適用每天銀行隨時隨地的更改提撥金額。
library(ggplot2)
plot10 = ggplot(Return_2, aes(x=date, y=APPLreturn)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=ForecastVaR_1),colour="red")+ ggtitle("APPLE報酬 與 VaR(0.01) 關係")
plot10
VaR(0.01)檢定
Ho : p=0.01 v.s. H1 : p =! 0.01 在unconditional 情況下，拒絕Ho， 但在conditional 的情況下，不拒絕Ho。
Test = cbind(Return_1$APPLreturn,Return_1$ForecastVaR_1)
Test = na.omit(Test)
actual = as.numeric(Test$APPLreturn)
VaR = as.numeric(Test$ForecastVaR_1)
VaRTest(alpha = 0.01, actual, VaR, conf.level = 0.99)## $expected.exceed
## [1] 5
##
## $actual.exceed
## [1] 12
##
## $uc.H0
## [1] "Correct Exceedances"
##
## $uc.LRstat
## [1] 7.082274
##
## $uc.critical
## [1] 6.634897
##
## $uc.LRp
## [1] 0.007785016
##
## $uc.Decision
## [1] "Reject H0"
##
## $cc.H0
## [1] "Correct Exceedances & Independent"
##
## $cc.LRstat
## [1] 8.237305
##
## $cc.critical
## [1] 9.21034
##
## $cc.LRp
## [1] 0.01626642
##
## $cc.Decision
## [1] "Fail to Reject H0"#VaRloss(alpha = 0.01, actual, VaR)
#VaRDurTest(alpha=0.01, actual, VaR, conf.level = 0.99)APPLE報酬 與 VaR(0.05) 關係
plot11 = ggplot(Return_2, aes(x=date, y=APPLreturn)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
geom_line(aes(y=ForecastVaR_2),colour="red")+ ggtitle("APPLE報酬 與 VaR(0.05) 關係")
plot11
VaR(0.05)檢定
Ho : p=0.05 v.s. H1 : p =! 0.05 在unconditional 情況下，不拒絕Ho， 但在conditional 的情況下，不拒絕Ho。
Test1 = cbind(Return_1$APPLreturn,Return_1$ForecastVaR_2)
Test1 = na.omit(Test1)
actual1 = as.numeric(Test1$APPLreturn)
VaR1 = as.numeric(Test1$ForecastVaR_2)
VaRTest(alpha = 0.05, actual1, VaR1, conf.level = 0.95)## $expected.exceed
## [1] 25
##
## $actual.exceed
## [1] 34
##
## $uc.H0
## [1] "Correct Exceedances"
##
## $uc.LRstat
## [1] 3.042461
##
## $uc.critical
## [1] 3.841459
##
## $uc.LRp
## [1] 0.08111288
##
## $uc.Decision
## [1] "Fail to Reject H0"
##
## $cc.H0
## [1] "Correct Exceedances & Independent"
##
## $cc.LRstat
## [1] 4.362975
##
## $cc.critical
## [1] 5.991465
##
## $cc.LRp
## [1] 0.1128735
##
## $cc.Decision
## [1] "Fail to Reject H0"#VaRloss(alpha = 0.05, actual1, VaR1)
#VaRDurTest(alpha=0.05, actual1, VaR1, conf.level = 0.95)library(gridExtra)
grid.arrange(plot10,plot11,nrow=2,ncol=1)
資產組合(FAAG)
library(rugarch)
library(rmgarch)
Attaching package: 'rmgarch'The following objects are masked from 'package:xts':
first, lastPortfolio = cbind(Return_1[,1:4])利用資產組合中的所有資產的報酬率資料建構多變量 copula garch
先決定每個marginal模型，決定標準殘差都通過
APPLE模型(省略中間流程)
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
APPLEspec = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="std")
APPLEmodelfit = ugarchfit(spec=APPLEspec, data=Portfolio$APPLreturn, solver="hybrid")
APPLEmodelfit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000845 0.001580 0.534673 0.592876
## archm 0.001054 0.121445 0.008682 0.993073
## omega 0.000006 0.000001 7.742071 0.000000
## alpha1 0.006800 0.008395 0.809986 0.417948
## beta1 0.898503 0.019019 47.241416 0.000000
## gamma1 0.148691 0.042491 3.499350 0.000466
## shape 3.857120 0.535156 7.207475 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.000845 0.001773 0.47644 0.633758
## archm 0.001054 0.133813 0.00788 0.993713
## omega 0.000006 0.000001 7.34199 0.000000
## alpha1 0.006800 0.011111 0.61204 0.540512
## beta1 0.898503 0.020692 43.42228 0.000000
## gamma1 0.148691 0.043776 3.39662 0.000682
## shape 3.857120 0.481052 8.01809 0.000000
##
## LogLikelihood : 2214.858
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.8564
## Bayes -5.8134
## Shibata -5.8566
## Hannan-Quinn -5.8398
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7828 0.3763
## Lag[2*(p+q)+(p+q)-1][2] 1.3065 0.4087
## Lag[4*(p+q)+(p+q)-1][5] 2.4602 0.5144
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.04727 0.8279
## Lag[2*(p+q)+(p+q)-1][5] 0.73990 0.9151
## Lag[4*(p+q)+(p+q)-1][9] 0.96233 0.9878
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.0003016 0.500 2.000 0.9861
## ARCH Lag[5] 0.0730800 1.440 1.667 0.9915
## ARCH Lag[7] 0.2014689 2.315 1.543 0.9970
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.8171
## Individual Statistics:
## mu 0.03386
## archm 0.03831
## omega 0.63691
## alpha1 0.44430
## beta1 0.49240
## gamma1 0.46999
## shape 0.90445
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 1.7679 0.07749 *
## Negative Sign Bias 1.0126 0.31160
## Positive Sign Bias 0.4482 0.65412
## Joint Effect 3.4272 0.33033
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 18.20 0.5090
## 2 30 22.58 0.7955
## 3 40 36.98 0.5623
## 4 50 38.97 0.8469
##
##
## Elapsed time : 1.12249FB模型(省略中間流程)
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
FBspec = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="std")
FBmodelfit = ugarchfit(spec=FBspec, data=Portfolio$FBreturn, solver="hybrid")
FBmodelfit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000855 0.000956 -0.89375 0.371456
## archm 0.149240 0.074235 2.01038 0.044391
## omega 0.000004 0.000002 2.00537 0.044924
## alpha1 0.016057 0.007776 2.06485 0.038937
## beta1 0.924018 0.015062 61.34760 0.000000
## gamma1 0.082401 0.027974 2.94558 0.003224
## shape 4.170360 0.620011 6.72626 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000855 0.002693 -0.31734 0.750985
## archm 0.149240 0.200326 0.74499 0.456279
## omega 0.000004 0.000005 0.93237 0.351145
## alpha1 0.016057 0.026286 0.61086 0.541291
## beta1 0.924018 0.017452 52.94537 0.000000
## gamma1 0.082401 0.040003 2.05986 0.039412
## shape 4.170360 0.573118 7.27662 0.000000
##
## LogLikelihood : 2200.831
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.8192
## Bayes -5.7762
## Shibata -5.8194
## Hannan-Quinn -5.8026
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.120 0.28997
## Lag[2*(p+q)+(p+q)-1][2] 1.662 0.32549
## Lag[4*(p+q)+(p+q)-1][5] 6.354 0.07416
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.8958 0.3439
## Lag[2*(p+q)+(p+q)-1][5] 2.3676 0.5345
## Lag[4*(p+q)+(p+q)-1][9] 3.2502 0.7170
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.7756 0.500 2.000 0.3785
## ARCH Lag[5] 1.5694 1.440 1.667 0.5742
## ARCH Lag[7] 1.9233 2.315 1.543 0.7336
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.4982
## Individual Statistics:
## mu 0.03975
## archm 0.04096
## omega 0.32001
## alpha1 0.72669
## beta1 0.61114
## gamma1 0.51297
## shape 0.73778
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.07449 0.94064
## Negative Sign Bias 1.73638 0.08291 *
## Positive Sign Bias 0.07191 0.94269
## Joint Effect 4.05634 0.25544
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 35.23 0.0131
## 2 30 38.41 0.1134
## 3 40 54.91 0.0469
## 4 50 47.72 0.5249
##
##
## Elapsed time : 1.504376AMAZON模型(省略中間流程)
ARMA_p = 0
ARMA_q = 0
GARCH_q = 1
GARCH_p = 1
AMAZONspec = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="std")
AMAZONmodelfit = ugarchfit(spec=AMAZONspec, data=Portfolio$AMZNreturn, solver="hybrid")
AMAZONmodelfit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000857 0.001792 -0.47797 0.632669
## archm 0.141135 0.125875 1.12123 0.262190
## omega 0.000018 0.000005 3.32069 0.000898
## alpha1 0.006736 0.009387 0.71762 0.472989
## beta1 0.828141 0.039972 20.71782 0.000000
## gamma1 0.254134 0.073804 3.44338 0.000574
## shape 3.758818 0.475936 7.89773 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.000857 0.001877 -0.45639 0.648110
## archm 0.141135 0.137862 1.02374 0.305956
## omega 0.000018 0.000006 3.19283 0.001409
## alpha1 0.006736 0.008520 0.79062 0.429164
## beta1 0.828141 0.044488 18.61482 0.000000
## gamma1 0.254134 0.074550 3.40893 0.000652
## shape 3.758818 0.562202 6.68588 0.000000
##
## LogLikelihood : 2149.452
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.6829
## Bayes -5.6400
## Shibata -5.6831
## Hannan-Quinn -5.6664
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.138 0.1437
## Lag[2*(p+q)+(p+q)-1][2] 2.930 0.1466
## Lag[4*(p+q)+(p+q)-1][5] 4.958 0.1565
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.003312 0.9541
## Lag[2*(p+q)+(p+q)-1][5] 0.339051 0.9795
## Lag[4*(p+q)+(p+q)-1][9] 0.535518 0.9981
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2491 0.500 2.000 0.6177
## ARCH Lag[5] 0.3406 1.440 1.667 0.9293
## ARCH Lag[7] 0.3972 2.315 1.543 0.9867
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 3.4558
## Individual Statistics:
## mu 0.04221
## archm 0.04874
## omega 1.71187
## alpha1 0.56285
## beta1 1.02856
## gamma1 0.90170
## shape 0.64875
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 2.096 0.03639 **
## Negative Sign Bias 1.185 0.23648
## Positive Sign Bias 1.038 0.29954
## Joint Effect 4.469 0.21509
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 21.07 0.3331
## 2 30 30.69 0.3799
## 3 40 37.19 0.5525
## 4 50 48.79 0.4818
##
##
## Elapsed time : 1.194367GOOGLE模型(省略中間流程)
ARMA_p = 1
ARMA_q = 0
GARCH_q = 1
GARCH_p = 0
GOOGLEspec = ugarchspec(mean.model = list(armaOrder=c(ARMA_p,ARMA_q),
include.mean=TRUE,
archm=TRUE,
archpow=1,
archex=FALSE),
variance.model=list(model="gjrGARCH",
garchOrder=c(GARCH_q ,GARCH_p)),
distribution.model="std")
GOOGLEmodelfit = ugarchfit(spec=GOOGLEspec, data=Portfolio$GOOGLreturn, solver="hybrid")
GOOGLEmodelfit##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,0)
## Mean Model : ARFIMA(1,0,0)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.016139 0.008769 1.84055 0.065688
## ar1 -0.029814 0.044318 -0.67274 0.501111
## archm -1.136638 0.642958 -1.76783 0.077090
## omega 0.000170 0.000024 6.95046 0.000000
## alpha1 0.001668 0.008598 0.19401 0.846168
## gamma1 0.140069 0.090851 1.54174 0.123136
## shape 3.581548 0.514423 6.96227 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.016139 0.007602 2.12298 0.033756
## ar1 -0.029814 0.044863 -0.66456 0.506330
## archm -1.136638 0.539825 -2.10557 0.035242
## omega 0.000170 0.000029 5.94676 0.000000
## alpha1 0.001668 0.004853 0.34374 0.731039
## gamma1 0.140069 0.100049 1.40000 0.161512
## shape 3.581548 0.591262 6.05746 0.000000
##
## LogLikelihood : 2266.912
##
## Information Criteria
## ------------------------------------
##
## Akaike -5.9945
## Bayes -5.9515
## Shibata -5.9946
## Hannan-Quinn -5.9779
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.757 0.18497
## Lag[2*(p+q)+(p+q)-1][2] 1.916 0.24324
## Lag[4*(p+q)+(p+q)-1][5] 5.310 0.08285
## d.o.f=1
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2848 0.5936
## Lag[2*(p+q)+(p+q)-1][2] 0.3055 0.7927
## Lag[4*(p+q)+(p+q)-1][5] 2.2340 0.5643
## d.o.f=1
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[2] 0.04117 0.500 2.000 0.8392
## ARCH Lag[4] 2.34249 1.397 1.611 0.3698
## ARCH Lag[6] 3.14100 2.222 1.500 0.4448
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.263
## Individual Statistics:
## mu 0.02425
## ar1 0.06912
## archm 0.02608
## omega 1.28187
## alpha1 0.70060
## gamma1 0.38523
## shape 2.72920
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.69 1.9 2.35
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.36340 0.71641
## Negative Sign Bias 0.02572 0.97949
## Positive Sign Bias 2.22045 0.02669 **
## Joint Effect 5.47616 0.14007
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 12.26 0.8742
## 2 30 32.13 0.3143
## 3 40 44.20 0.2615
## 4 50 45.87 0.6009
##
##
## Elapsed time : 2.249566決定portfolio model
以下是運用copula工具，不同分配去描述資料的相關性。
一階估計的參數較準確，但由於參數過多，採用二階的做法較為迅速且損失一些精確度。 在time varying 情形下dcca1與dccb1分別代表dynamic ARCH 參數與 dynamic GARCH參數，由於不論二階或是一階的估計，這兩項參數的p value相當小，則意味著在copula下他們提供非常重要的資訊去描述DCC聯合密度模型。
在time not varying 情況下，c1代表APPLE 與 FB報酬的相關係數、c2代表APPLE 與 AMAZON報酬的相關係數、c3代表APPLE 與 GOOGLE報酬的相關係數、c4代表FB 與 AMAZON報酬的相關係數、c5代表FB 與 GOOGLE報酬的相關係數、c6代表AMAZON 與 GOOGLE報酬的相關係數。
#一階且Time varying
portfoliospec = cgarchspec(uspec = multispec(c(APPLEspec,FBspec,AMAZONspec,GOOGLEspec) ),VAR = TRUE ,lag = 1, lag.max = 4,
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL,
dccOrder = c(1,1), distribution.model = list(copula = c("mvt"), method = c("ML"),time.varying = TRUE), start.pars = list(), fixed.pars = list())
#一階且Time not varying
portfoliospec_1 = cgarchspec(uspec = multispec(c(APPLEspec,FBspec,AMAZONspec,GOOGLEspec) ),VAR = TRUE ,lag = 1, lag.max = 4,
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL,
distribution.model = list(copula = c("mvt"), method = c("ML"),time.varying = FALSE), start.pars = list(), fixed.pars = list())
#二階且Time varying
portfoliospec1 = cgarchspec(uspec = multispec(c(APPLEspec,FBspec,AMAZONspec,GOOGLEspec) ),VAR = TRUE ,lag = 1, lag.max = 4,
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL,
dccOrder = c(1,1), distribution.model = list(copula = c("mvt"), method = c("kendall"),
time.varying = TRUE, transformation = "spd"), start.pars = list(), fixed.pars = list())
#二階且Time not varying
portfoliospec1_1 = cgarchspec(uspec = multispec(c(APPLEspec,FBspec,AMAZONspec,GOOGLEspec) ),VAR = TRUE ,lag = 1, lag.max = 4,
lag.criterion = c("AIC", "HQ", "SC", "FPE"), external.regressors = NULL,
dccOrder = c(1,1), distribution.model = list(copula = c("mvt"), method = c("kendall"),
time.varying = FALSE, transformation = "spd"), start.pars = list(), fixed.pars = list())fit portfolio model
portfoliofit = cgarchfit(portfoliospec, data =Portfolio, fit.control = list(eval.se = TRUE, trace = TRUE), solver = "solnp")
portfoliofit##
## *-------------------------------------------------*
## * Copula GARCH Fit *
## *-------------------------------------------------*
##
## Distribution : mvt
## DCC Order : 1 1
## Asymmetric : FALSE
## No. of Parameters : 48
## [VAR GARCH DCC UncQ]: [20+19+3+6]
## No. of Series : 4
## No. of Observations : 754
## Log-Likelihood : 9490.323
## Av.Log-Likelihood : 12.587
##
## Optimal Parameters
## ---------------------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [APPLreturn].omega 0.000006 0.000001 9.47387 0.000000
## [APPLreturn].alpha1 0.003077 0.004881 0.63046 0.528392
## [APPLreturn].beta1 0.907895 0.017967 50.53258 0.000000
## [APPLreturn].gamma1 0.143450 0.041673 3.44228 0.000577
## [APPLreturn].shape 3.893015 0.537666 7.24059 0.000000
## [FBreturn].omega 0.000003 0.000005 0.56703 0.570693
## [FBreturn].alpha1 0.001288 0.012528 0.10284 0.918088
## [FBreturn].beta1 0.942248 0.028888 32.61680 0.000000
## [FBreturn].gamma1 0.089719 0.042482 2.11192 0.034693
## [FBreturn].shape 4.460844 0.870322 5.12551 0.000000
## [AMZNreturn].omega 0.000014 0.000003 4.54177 0.000006
## [AMZNreturn].alpha1 0.005017 0.008020 0.62563 0.531560
## [AMZNreturn].beta1 0.852640 0.028397 30.02619 0.000000
## [AMZNreturn].gamma1 0.220777 0.048376 4.56380 0.000005
## [AMZNreturn].shape 3.836365 0.493205 7.77843 0.000000
## [GOOGLreturn].omega 0.000162 0.000023 6.93417 0.000000
## [GOOGLreturn].alpha1 0.017981 0.015100 1.19081 0.233727
## [GOOGLreturn].gamma1 0.189680 0.117745 1.61093 0.107195
## [GOOGLreturn].shape 3.665548 0.582991 6.28749 0.000000
## [Joint]dcca1 0.021773 0.007916 2.75050 0.005950
## [Joint]dccb1 0.903127 0.032596 27.70679 0.000000
## [Joint]mshape 7.247794 0.816173 8.88022 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -25.115
## Bayes -24.980
## Shibata -25.117
## Hannan-Quinn -25.063
##
##
## Elapsed time : 8.644318portfoliofit_1 = cgarchfit(portfoliospec_1, data =Portfolio, fit.control = list(eval.se = TRUE, trace = TRUE), solver = "solnp")
portfoliofit_1##
## *-------------------------------------------------*
## * Copula GARCH Fit *
## *-------------------------------------------------*
##
## Distribution : mvt
## No. of Parameters : 46
## [VAR GARCH CC] : [20+19+7]
## No. of Series : 4
## No. of Observations : 754
## Log-Likelihood : 9487.661
## Av.Log-Likelihood : 12.583
##
## Optimal Parameters
## ---------------------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [APPLreturn].omega 0.000006 0.000001 9.44557 0.000000
## [APPLreturn].alpha1 0.003077 0.004907 0.62710 0.530592
## [APPLreturn].beta1 0.907895 0.018211 49.85368 0.000000
## [APPLreturn].gamma1 0.143450 0.041892 3.42427 0.000616
## [APPLreturn].shape 3.893015 0.538218 7.23315 0.000000
## [FBreturn].omega 0.000003 0.000005 0.56994 0.568719
## [FBreturn].alpha1 0.001288 0.012467 0.10335 0.917687
## [FBreturn].beta1 0.942248 0.028867 32.64074 0.000000
## [FBreturn].gamma1 0.089719 0.042254 2.12332 0.033727
## [FBreturn].shape 4.460844 0.867598 5.14160 0.000000
## [AMZNreturn].omega 0.000014 0.000003 4.47572 0.000008
## [AMZNreturn].alpha1 0.005017 0.008014 0.62607 0.531267
## [AMZNreturn].beta1 0.852640 0.028870 29.53379 0.000000
## [AMZNreturn].gamma1 0.220777 0.050419 4.37887 0.000012
## [AMZNreturn].shape 3.836365 0.495385 7.74421 0.000000
## [GOOGLreturn].omega 0.000162 0.000024 6.82913 0.000000
## [GOOGLreturn].alpha1 0.017981 0.015119 1.18928 0.234329
## [GOOGLreturn].gamma1 0.189680 0.117884 1.60903 0.107609
## [GOOGLreturn].shape 3.665548 0.586304 6.25195 0.000000
## [Joint]C1 0.592311 0.043187 13.71487 0.000000
## [Joint]C2 0.607999 0.049033 12.39981 0.000000
## [Joint]C3 0.732164 0.053513 13.68201 0.000000
## [Joint]C4 0.654015 0.046854 13.95866 0.000000
## [Joint]C5 0.751350 0.047556 15.79916 0.000000
## [Joint]C6 0.455819 0.043182 10.55589 0.000000
## [Joint]mshape 7.149139 0.821774 8.69964 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -25.097
## Bayes -24.938
## Shibata -25.100
## Hannan-Quinn -25.036
##
##
## Elapsed time : 14.51002portfoliofit1 =cgarchfit(portfoliospec1, data =Portfolio, spd.control = list(lower = 0.1, upper = 0.9, type = "pwm",
kernel = "epanech"), fit.control = list(eval.se = TRUE, trace = TRUE), solver = "solnp")
portfoliofit1##
## *-------------------------------------------------*
## * Copula GARCH Fit *
## *-------------------------------------------------*
##
## Distribution : mvt
## DCC Order : 1 1
## Asymmetric : FALSE
## No. of Parameters : 48
## [VAR GARCH DCC UncQ]: [20+19+3+6]
## No. of Series : 4
## No. of Observations : 754
## Log-Likelihood : 9485.842
## Av.Log-Likelihood : 12.581
##
## Optimal Parameters
## ---------------------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [APPLreturn].omega 0.000006 0.000001 9.47547 0.000000
## [APPLreturn].alpha1 0.003077 0.004884 0.63005 0.528662
## [APPLreturn].beta1 0.907895 0.017942 50.60237 0.000000
## [APPLreturn].gamma1 0.143450 0.041575 3.45042 0.000560
## [APPLreturn].shape 3.893015 0.531381 7.32622 0.000000
## [FBreturn].omega 0.000003 0.000005 0.56034 0.575248
## [FBreturn].alpha1 0.001288 0.012470 0.10332 0.917706
## [FBreturn].beta1 0.942248 0.029080 32.40196 0.000000
## [FBreturn].gamma1 0.089719 0.043105 2.08139 0.037398
## [FBreturn].shape 4.460844 0.870752 5.12298 0.000000
## [AMZNreturn].omega 0.000014 0.000003 4.50569 0.000007
## [AMZNreturn].alpha1 0.005017 0.008013 0.62611 0.531244
## [AMZNreturn].beta1 0.852640 0.028445 29.97455 0.000000
## [AMZNreturn].gamma1 0.220777 0.048760 4.52780 0.000006
## [AMZNreturn].shape 3.836365 0.497967 7.70405 0.000000
## [GOOGLreturn].omega 0.000162 0.000023 7.04506 0.000000
## [GOOGLreturn].alpha1 0.017981 0.015030 1.19631 0.231574
## [GOOGLreturn].gamma1 0.189680 0.117684 1.61177 0.107012
## [GOOGLreturn].shape 3.665548 0.573019 6.39690 0.000000
## [Joint]dcca1 0.025323 0.010293 2.46027 0.013883
## [Joint]dccb1 0.891588 0.041314 21.58086 0.000000
## [Joint]mshape 6.829405 0.807542 8.45702 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -25.103
## Bayes -24.968
## Shibata -25.105
## Hannan-Quinn -25.051
##
##
## Elapsed time : 10.92335portfoliofit1_1 =cgarchfit(portfoliospec1_1, data =Portfolio, spd.control = list(lower = 0.1, upper = 0.9, type = "pwm",
kernel = "epanech"), fit.control = list(eval.se = TRUE, trace = TRUE), solver = "solnp")
portfoliofit1_1##
## *-------------------------------------------------*
## * Copula GARCH Fit *
## *-------------------------------------------------*
##
## Distribution : mvt
## No. of Parameters : 40
## [VAR GARCH CC] : [20+19+1]
## No. of Series : 4
## No. of Observations : 754
## Log-Likelihood : 9489.19
## Av.Log-Likelihood : 12.585
##
## Optimal Parameters
## ---------------------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [APPLreturn].omega 0.000006 0.000001 9.48023 0.000000
## [APPLreturn].alpha1 0.003077 0.004888 0.62954 0.528994
## [APPLreturn].beta1 0.907895 0.017905 50.70732 0.000000
## [APPLreturn].gamma1 0.143450 0.041677 3.44197 0.000577
## [APPLreturn].shape 3.893015 0.530341 7.34059 0.000000
## [FBreturn].omega 0.000003 0.000005 0.56300 0.573434
## [FBreturn].alpha1 0.001288 0.012474 0.10329 0.917733
## [FBreturn].beta1 0.942248 0.028983 32.51042 0.000000
## [FBreturn].gamma1 0.089719 0.042817 2.09541 0.036135
## [FBreturn].shape 4.460844 0.866939 5.14551 0.000000
## [AMZNreturn].omega 0.000014 0.000003 4.41063 0.000010
## [AMZNreturn].alpha1 0.005017 0.008030 0.62483 0.532083
## [AMZNreturn].beta1 0.852640 0.028202 30.23363 0.000000
## [AMZNreturn].gamma1 0.220777 0.047329 4.66472 0.000003
## [AMZNreturn].shape 3.836365 0.490551 7.82052 0.000000
## [GOOGLreturn].omega 0.000162 0.000023 7.05170 0.000000
## [GOOGLreturn].alpha1 0.017981 0.014949 1.20278 0.229061
## [GOOGLreturn].gamma1 0.189680 0.117950 1.60814 0.107804
## [GOOGLreturn].shape 3.665548 0.573058 6.39646 0.000000
## [Joint]mshape 6.647865 0.851810 7.80440 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -25.117
## Bayes -24.995
## Shibata -25.119
## Hannan-Quinn -25.070
##
##
## Elapsed time : 6.689686rcor and plot
conditional correlation array with third dimensionlabels the time index.
#rcor(portfoliofit)
portfoliocor = Portfolio
rcor(portfoliofit)[2,1,1]## [1] 0.4857259portfoliocor$APPLEandFB = NA
for (i in 1:DataSize){
portfoliocor$APPLEandFB[i] = rcor(portfoliofit)[2,1,i]
}
portfoliocor$APPLEandAMAZON = NA
for (i in 1:DataSize){
portfoliocor$APPLEandAMAZON[i] = rcor(portfoliofit)[3,1,i]
}
portfoliocor$APPLEandGOOGLE = NA
for (i in 1:DataSize){
portfoliocor$APPLEandGOOGLE[i] = rcor(portfoliofit)[4,1,i]
}
portfoliocor$FBandAMAZON = NA
for (i in 1:DataSize){
portfoliocor$FBandAMAZON[i] = rcor(portfoliofit)[3,2,i]
}
portfoliocor$FBandGOOGLE = NA
for (i in 1:DataSize){
portfoliocor$FBandGOOGLE[i] = rcor(portfoliofit)[4,2,i]
}
portfoliocor$AMAZONandGOOGLE = NA
for (i in 1:DataSize){
portfoliocor$AMAZONandGOOGLE[i] = rcor(portfoliofit)[4,3,i]
}
portfoliocor_1 = data.frame(date = index(portfoliocor), coredata(portfoliocor))
plot12 = ggplot(portfoliocor_1, aes(x=date, y=APPLEandFB)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("APPLEandFB correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot12
plot13 = ggplot(portfoliocor_1, aes(x=date, y=APPLEandAMAZON)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("APPLEandAMAZON correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot13
plot14 = ggplot(portfoliocor_1, aes(x=date, y=APPLEandGOOGLE)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("APPLEandGOOGLE correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot14
plot15 = ggplot(portfoliocor_1, aes(x=date, y=FBandAMAZON)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("FBandAMAZON correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot15
plot16 = ggplot(portfoliocor_1, aes(x=date, y=FBandGOOGLE)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("FBandGOOGLE correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot16
plot17 = ggplot(portfoliocor_1, aes(x=date, y=AMAZONandGOOGLE)) +
geom_line() +
xlab("")+
scale_x_date(date_labels = "%Y %b %d")+
ggtitle("AMAZONandGOOGLE correlation by copula GARCH")+
theme_economist() + scale_colour_economist()
plot17
grid.arrange(plot12,plot13,plot14,plot15,plot16,plot17,nrow=3,ncol=2)
likelihood
the joint likelihood
likelihood(portfoliofit)## [1] 9490.323cordist
Given an array of correlation snapshots in time, returns a matrix of some rolling distance measure on the correlations.
這是預設情況下，選定apple與fb的correlation隨時間經過的熱力圖
cordist(R=rcor(portfoliofit), distance = c("ma","ms","meda","meds","eigen", "cmd"), n = 25,
plot = TRUE, dates = NULL, title = NULL)
dcc garch
dcc garch較copula沒彈性，尤其在分配的選用上，只能選定多為常態分配。
dcc test
A test of non-constant correlation based on Engle and Sheppard (2001).
DCCtest(Portfolio, garchOrder = c(1,1), n.lags = 1, solver = "solnp",
solver.control = list(), cluster = NULL, Z = NULL)## $H0
## [1] "Constant Probability"
##
## $p.value
## [1] 0.9845279
##
## $statistic
## [1] 0.03118601只能選用多為常態分配作為模型依據，否則無法使用
standardspec = ugarchspec(mean.model = list(armaOrder = c(0,0)),
variance.model = list(garchOrder = c(1,1),
model = "sGARCH"),
distribution.model = "norm" )
dcc=dccspec(uspec = multispec(replicate(4,standardspec)),distribution = "mvnorm")dcc fit
dccfit = dccfit(dcc, data =Portfolio)
dccfit##
## *---------------------------------*
## * DCC GARCH Fit *
## *---------------------------------*
##
## Distribution : mvnorm
## Model : DCC(1,1)
## No. Parameters : 24
## [VAR GARCH DCC UncQ] : [0+16+2+6]
## No. Series : 4
## No. Obs. : 754
## Log-Likelihood : 9003.831
## Av.Log-Likelihood : 11.94
##
## Optimal Parameters
## -----------------------------------
## Estimate Std. Error t value Pr(>|t|)
## [APPLreturn].mu 0.001045 0.000506 2.06647 0.038784
## [APPLreturn].omega 0.000002 0.000002 0.72566 0.468045
## [APPLreturn].alpha1 0.017960 0.004134 4.34414 0.000014
## [APPLreturn].beta1 0.972665 0.006092 159.65464 0.000000
## [FBreturn].mu 0.001291 0.000474 2.72528 0.006425
## [FBreturn].omega 0.000010 0.000003 3.37301 0.000744
## [FBreturn].alpha1 0.099713 0.017856 5.58438 0.000000
## [FBreturn].beta1 0.863100 0.027109 31.83864 0.000000
## [AMZNreturn].mu 0.001861 0.000768 2.42443 0.015332
## [AMZNreturn].omega 0.000002 0.000004 0.57501 0.565284
## [AMZNreturn].alpha1 0.009056 0.006891 1.31423 0.188769
## [AMZNreturn].beta1 0.982110 0.014328 68.54447 0.000000
## [GOOGLreturn].mu 0.000793 0.000462 1.71671 0.086031
## [GOOGLreturn].omega 0.000031 0.000013 2.42120 0.015469
## [GOOGLreturn].alpha1 0.241749 0.146880 1.64590 0.099785
## [GOOGLreturn].beta1 0.618876 0.128424 4.81902 0.000001
## [Joint]dcca1 0.004484 0.007976 0.56210 0.574045
## [Joint]dccb1 0.902632 0.047379 19.05147 0.000000
##
## Information Criteria
## ---------------------
##
## Akaike -23.819
## Bayes -23.672
## Shibata -23.821
## Hannan-Quinn -23.762
##
##
## Elapsed time : 2.66779dcc news impact covariance
在預設情況下是選定APPLE與FB報酬去做news impact covariance圖，這個概念有點像講義裏頭提到news impact cure，又類似gjr GARCH模型，去解釋shock狀況。 橫軸座標shock[z_1]是APPLE報酬std. residual 與shock[z_1]是 FB報酬std. residual….. 圖形有在解釋倆倆之間風險溢酬的covariance變化狀況。
nisurface(dccfit)
## $nisurface
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.249582e-04 1.245384e-04 1.241037e-04 1.236537e-04 1.231883e-04
## [2,] 1.245333e-04 1.241313e-04 1.237146e-04 1.232828e-04 1.228357e-04
## [3,] 1.240935e-04 1.237095e-04 1.233109e-04 1.228975e-04 1.224690e-04
## [4,] 1.236385e-04 1.232727e-04 1.228925e-04 1.224976e-04 1.220879e-04
## [5,] 1.231681e-04 1.228207e-04 1.224591e-04 1.220830e-04 1.216922e-04
## [6,] 1.226823e-04 1.223534e-04 1.220105e-04 1.216534e-04 1.212817e-04
## [7,] 1.221806e-04 1.218705e-04 1.215465e-04 1.212085e-04 1.208562e-04
## [8,] 1.216630e-04 1.213718e-04 1.210669e-04 1.207483e-04 1.204155e-04
## [9,] 1.211293e-04 1.208572e-04 1.205716e-04 1.202724e-04 1.199594e-04
## [10,] 1.205793e-04 1.203264e-04 1.200603e-04 1.197809e-04 1.194877e-04
## [11,] 1.200129e-04 1.197794e-04 1.195330e-04 1.192734e-04 1.190003e-04
## [12,] 1.194300e-04 1.192161e-04 1.189894e-04 1.187498e-04 1.184970e-04
## [13,] 1.188303e-04 1.186361e-04 1.184295e-04 1.182101e-04 1.179777e-04
## [14,] 1.182138e-04 1.180395e-04 1.178530e-04 1.176540e-04 1.174421e-04
## [15,] 1.175804e-04 1.174262e-04 1.172600e-04 1.170814e-04 1.168903e-04
## [16,] 1.169301e-04 1.167960e-04 1.166502e-04 1.164923e-04 1.163221e-04
## [17,] 1.162626e-04 1.161489e-04 1.160237e-04 1.158866e-04 1.157375e-04
## [18,] 1.155781e-04 1.154849e-04 1.153803e-04 1.152642e-04 1.151362e-04
## [19,] 1.148764e-04 1.148038e-04 1.147201e-04 1.146250e-04 1.145184e-04
## [20,] 1.141575e-04 1.141056e-04 1.140429e-04 1.139691e-04 1.138839e-04
## [21,] 1.134215e-04 1.133905e-04 1.133488e-04 1.132963e-04 1.132327e-04
## [22,] 1.126683e-04 1.126582e-04 1.126378e-04 1.126068e-04 1.125649e-04
## [23,] 1.118980e-04 1.119090e-04 1.119099e-04 1.119004e-04 1.118803e-04
## [24,] 1.111107e-04 1.111428e-04 1.111651e-04 1.111773e-04 1.111791e-04
## [25,] 1.103064e-04 1.103597e-04 1.104035e-04 1.104375e-04 1.104613e-04
## [26,] 1.094851e-04 1.095598e-04 1.096252e-04 1.096810e-04 1.097270e-04
## [27,] 1.086472e-04 1.087433e-04 1.088303e-04 1.089080e-04 1.089762e-04
## [28,] 1.077925e-04 1.079101e-04 1.080189e-04 1.081186e-04 1.082090e-04
## [29,] 1.069214e-04 1.070605e-04 1.071911e-04 1.073129e-04 1.074256e-04
## [30,] 1.060340e-04 1.061947e-04 1.063472e-04 1.064911e-04 1.066262e-04
## [31,] 1.051305e-04 1.053128e-04 1.054872e-04 1.056533e-04 1.058108e-04
## [32,] 1.042110e-04 1.044150e-04 1.046113e-04 1.047996e-04 1.049797e-04
## [33,] 1.032759e-04 1.035016e-04 1.037199e-04 1.039305e-04 1.041330e-04
## [34,] 1.023254e-04 1.025729e-04 1.028131e-04 1.030460e-04 1.032710e-04
## [35,] 1.013598e-04 1.016290e-04 1.018912e-04 1.021463e-04 1.023940e-04
## [36,] 1.003793e-04 1.006702e-04 1.009545e-04 1.012319e-04 1.015021e-04
## [37,] 9.938431e-05 9.969695e-05 1.000033e-04 1.003029e-04 1.005957e-04
## [38,] 9.837512e-05 9.870948e-05 9.903779e-05 9.935975e-05 9.967508e-05
## [39,] 9.735209e-05 9.770815e-05 9.805843e-05 9.840265e-05 9.874051e-05
## [40,] 9.631558e-05 9.669330e-05 9.706553e-05 9.743198e-05 9.779235e-05
## [41,] 9.526599e-05 9.566533e-05 9.605947e-05 9.644810e-05 9.683095e-05
## [42,] 9.420370e-05 9.462462e-05 9.504062e-05 9.545140e-05 9.585666e-05
## [43,] 9.312913e-05 9.357157e-05 9.400938e-05 9.444224e-05 9.486988e-05
## [44,] 9.204271e-05 9.250661e-05 9.296616e-05 9.342105e-05 9.387100e-05
## [45,] 9.094489e-05 9.143018e-05 9.191139e-05 9.238824e-05 9.286042e-05
## [46,] 8.983613e-05 9.034271e-05 9.084551e-05 9.134423e-05 9.183856e-05
## [47,] 8.871688e-05 8.924467e-05 8.976897e-05 9.028947e-05 9.080587e-05
## [48,] 8.758762e-05 8.813653e-05 8.868223e-05 8.922441e-05 8.976278e-05
## [49,] 8.644885e-05 8.701877e-05 8.758576e-05 8.814952e-05 8.870975e-05
## [50,] 8.530106e-05 8.589187e-05 8.648005e-05 8.706527e-05 8.764725e-05
## [51,] 8.414475e-05 8.475634e-05 8.536557e-05 8.597215e-05 8.657576e-05
## [52,] 8.298044e-05 8.361267e-05 8.424284e-05 8.487063e-05 8.549574e-05
## [53,] 8.180863e-05 8.246138e-05 8.311234e-05 8.376121e-05 8.440768e-05
## [54,] 8.062986e-05 8.130298e-05 8.197460e-05 8.264440e-05 8.331209e-05
## [55,] 7.944464e-05 8.013799e-05 8.083011e-05 8.152070e-05 8.220946e-05
## [56,] 7.825351e-05 7.896692e-05 7.967938e-05 8.039061e-05 8.110028e-05
## [57,] 7.705698e-05 7.779029e-05 7.852295e-05 7.925464e-05 7.998505e-05
## [58,] 7.585559e-05 7.660864e-05 7.736131e-05 7.811330e-05 7.886429e-05
## [59,] 7.464986e-05 7.542248e-05 7.619499e-05 7.696710e-05 7.773850e-05
## [60,] 7.344032e-05 7.423232e-05 7.502450e-05 7.581656e-05 7.660817e-05
## [61,] 7.222749e-05 7.303869e-05 7.385035e-05 7.466216e-05 7.547381e-05
## [62,] 7.101188e-05 7.184211e-05 7.267306e-05 7.350443e-05 7.433591e-05
## [63,] 6.979403e-05 7.064307e-05 7.149311e-05 7.234385e-05 7.319498e-05
## [64,] 6.857442e-05 6.944208e-05 7.031102e-05 7.118093e-05 7.205149e-05
## [65,] 6.735356e-05 6.823964e-05 6.912728e-05 7.001615e-05 7.090595e-05
## [66,] 6.613195e-05 6.703625e-05 6.794237e-05 6.885000e-05 6.975882e-05
## [67,] 6.491007e-05 6.583238e-05 6.675677e-05 6.768294e-05 6.861057e-05
## [68,] 6.368841e-05 6.462851e-05 6.557097e-05 6.651546e-05 6.746168e-05
## [69,] 6.246742e-05 6.342511e-05 6.438540e-05 6.534801e-05 6.631259e-05
## [70,] 6.124758e-05 6.222263e-05 6.320055e-05 6.418103e-05 6.516376e-05
## [71,] 6.002932e-05 6.102151e-05 6.201683e-05 6.301498e-05 6.401563e-05
## [72,] 5.881309e-05 5.982220e-05 6.083469e-05 6.185028e-05 6.286862e-05
## [73,] 5.759931e-05 5.862511e-05 5.965456e-05 6.068734e-05 6.172315e-05
## [74,] 5.638839e-05 5.743066e-05 5.847683e-05 5.952659e-05 6.057963e-05
## [75,] 5.518074e-05 5.623926e-05 5.730192e-05 5.836842e-05 5.943845e-05
## [76,] 5.397675e-05 5.505128e-05 5.613020e-05 5.721321e-05 5.830000e-05
## [77,] 5.277679e-05 5.386710e-05 5.496206e-05 5.606134e-05 5.716465e-05
## [78,] 5.158123e-05 5.268709e-05 5.379784e-05 5.491317e-05 5.603276e-05
## [79,] 5.039041e-05 5.151160e-05 5.263791e-05 5.376905e-05 5.490468e-05
## [80,] 4.920468e-05 5.034096e-05 5.148260e-05 5.262931e-05 5.378075e-05
## [81,] 4.802435e-05 4.917549e-05 5.033224e-05 5.149427e-05 5.266129e-05
## [82,] 4.684974e-05 4.801552e-05 4.918712e-05 5.036426e-05 5.154661e-05
## [83,] 4.568115e-05 4.686132e-05 4.804756e-05 4.923956e-05 5.043700e-05
## [84,] 4.451885e-05 4.571319e-05 4.691383e-05 4.812046e-05 4.933275e-05
## [85,] 4.336311e-05 4.457140e-05 4.578620e-05 4.700722e-05 4.823414e-05
## [86,] 4.221420e-05 4.343620e-05 4.466494e-05 4.590012e-05 4.714143e-05
## [87,] 4.107235e-05 4.230783e-05 4.355028e-05 4.479940e-05 4.605485e-05
## [88,] 3.993779e-05 4.118654e-05 4.244247e-05 4.370528e-05 4.497465e-05
## [89,] 3.881074e-05 4.007252e-05 4.134171e-05 4.261799e-05 4.390104e-05
## [90,] 3.769140e-05 3.896600e-05 4.024821e-05 4.153773e-05 4.283424e-05
## [91,] 3.657997e-05 3.786716e-05 3.916218e-05 4.046471e-05 4.177445e-05
## [92,] 3.547662e-05 3.677619e-05 3.808378e-05 3.939911e-05 4.072184e-05
## [93,] 3.438152e-05 3.569325e-05 3.701320e-05 3.834109e-05 3.967660e-05
## [94,] 3.329483e-05 3.461849e-05 3.595059e-05 3.729082e-05 3.863888e-05
## [95,] 3.221668e-05 3.355207e-05 3.489610e-05 3.624846e-05 3.760884e-05
## [96,] 3.114721e-05 3.249412e-05 3.384985e-05 3.521413e-05 3.658662e-05
## [97,] 3.008654e-05 3.144475e-05 3.281199e-05 3.418796e-05 3.557235e-05
## [98,] 2.903478e-05 3.040409e-05 3.178263e-05 3.317008e-05 3.456614e-05
## [99,] 2.799203e-05 2.937224e-05 3.076186e-05 3.216059e-05 3.356811e-05
## [100,] 2.695838e-05 2.834928e-05 2.974978e-05 3.115958e-05 3.257836e-05
## [,6] [,7] [,8] [,9] [,10]
## [1,] 1.227072e-04 1.222103e-04 1.216973e-04 1.211681e-04 1.206225e-04
## [2,] 1.223732e-04 1.218950e-04 1.214010e-04 1.208909e-04 1.203645e-04
## [3,] 1.220252e-04 1.215660e-04 1.210911e-04 1.206003e-04 1.200934e-04
## [4,] 1.216631e-04 1.212230e-04 1.207674e-04 1.202961e-04 1.198090e-04
## [5,] 1.212866e-04 1.208658e-04 1.204298e-04 1.199782e-04 1.195110e-04
## [6,] 1.208954e-04 1.204942e-04 1.200779e-04 1.196463e-04 1.191992e-04
## [7,] 1.204895e-04 1.201080e-04 1.197116e-04 1.193001e-04 1.188733e-04
## [8,] 1.200685e-04 1.197070e-04 1.193307e-04 1.189396e-04 1.185333e-04
## [9,] 1.196323e-04 1.192909e-04 1.189350e-04 1.185644e-04 1.181788e-04
## [10,] 1.191807e-04 1.188597e-04 1.185243e-04 1.181743e-04 1.178097e-04
## [11,] 1.187136e-04 1.184130e-04 1.180983e-04 1.177693e-04 1.174258e-04
## [12,] 1.182308e-04 1.179509e-04 1.176570e-04 1.173491e-04 1.170269e-04
## [13,] 1.177321e-04 1.174730e-04 1.172002e-04 1.169136e-04 1.166128e-04
## [14,] 1.172173e-04 1.169793e-04 1.167278e-04 1.164626e-04 1.161835e-04
## [15,] 1.166865e-04 1.164696e-04 1.162395e-04 1.159960e-04 1.157387e-04
## [16,] 1.161394e-04 1.159439e-04 1.157354e-04 1.155136e-04 1.152783e-04
## [17,] 1.155760e-04 1.154020e-04 1.152152e-04 1.150153e-04 1.148022e-04
## [18,] 1.149962e-04 1.148438e-04 1.146789e-04 1.145012e-04 1.143104e-04
## [19,] 1.143999e-04 1.142693e-04 1.141264e-04 1.139709e-04 1.138026e-04
## [20,] 1.137871e-04 1.136785e-04 1.135577e-04 1.134246e-04 1.132789e-04
## [21,] 1.131578e-04 1.130712e-04 1.129727e-04 1.128621e-04 1.127392e-04
## [22,] 1.125118e-04 1.124474e-04 1.123714e-04 1.122835e-04 1.121835e-04
## [23,] 1.118493e-04 1.118072e-04 1.117537e-04 1.116886e-04 1.116116e-04
## [24,] 1.111703e-04 1.111506e-04 1.111198e-04 1.110775e-04 1.110237e-04
## [25,] 1.104748e-04 1.104776e-04 1.104695e-04 1.104503e-04 1.104196e-04
## [26,] 1.097628e-04 1.097882e-04 1.098030e-04 1.098069e-04 1.097996e-04
## [27,] 1.090344e-04 1.090826e-04 1.091203e-04 1.091474e-04 1.091635e-04
## [28,] 1.082898e-04 1.083607e-04 1.084215e-04 1.084718e-04 1.085115e-04
## [29,] 1.075290e-04 1.076228e-04 1.077066e-04 1.077803e-04 1.078436e-04
## [30,] 1.067522e-04 1.068689e-04 1.069759e-04 1.070730e-04 1.071600e-04
## [31,] 1.059595e-04 1.060992e-04 1.062294e-04 1.063500e-04 1.064607e-04
## [32,] 1.051512e-04 1.053138e-04 1.054673e-04 1.056115e-04 1.057459e-04
## [33,] 1.043273e-04 1.045130e-04 1.046898e-04 1.048575e-04 1.050158e-04
## [34,] 1.034881e-04 1.036969e-04 1.038971e-04 1.040884e-04 1.042705e-04
## [35,] 1.026339e-04 1.028658e-04 1.030893e-04 1.033042e-04 1.035103e-04
## [36,] 1.017649e-04 1.020198e-04 1.022668e-04 1.025053e-04 1.027353e-04
## [37,] 1.008813e-04 1.011594e-04 1.014297e-04 1.016919e-04 1.019458e-04
## [38,] 9.998348e-05 1.002847e-04 1.005783e-04 1.008642e-04 1.011420e-04
## [39,] 9.907173e-05 9.939600e-05 9.971304e-05 1.000225e-04 1.003242e-04
## [40,] 9.814635e-05 9.849369e-05 9.883405e-05 9.916715e-05 9.949268e-05
## [41,] 9.720770e-05 9.757806e-05 9.794172e-05 9.829839e-05 9.864776e-05
## [42,] 9.625612e-05 9.664946e-05 9.703638e-05 9.741658e-05 9.778975e-05
## [43,] 9.529199e-05 9.570826e-05 9.611838e-05 9.652206e-05 9.691897e-05
## [44,] 9.431569e-05 9.475482e-05 9.518809e-05 9.561519e-05 9.603579e-05
## [45,] 9.332762e-05 9.378956e-05 9.424590e-05 9.469634e-05 9.514056e-05
## [46,] 9.232821e-05 9.281285e-05 9.329219e-05 9.376590e-05 9.423367e-05
## [47,] 9.131786e-05 9.182514e-05 9.232738e-05 9.282427e-05 9.331549e-05
## [48,] 9.029702e-05 9.082683e-05 9.135188e-05 9.187186e-05 9.238644e-05
## [49,] 8.926614e-05 8.981837e-05 9.036613e-05 9.090909e-05 9.144692e-05
## [50,] 8.822567e-05 8.880022e-05 8.937057e-05 8.993639e-05 9.049736e-05
## [51,] 8.717609e-05 8.777282e-05 8.836564e-05 8.895421e-05 8.953820e-05
## [52,] 8.611785e-05 8.673664e-05 8.735180e-05 8.796298e-05 8.856987e-05
## [53,] 8.505144e-05 8.569216e-05 8.632952e-05 8.696318e-05 8.759281e-05
## [54,] 8.397735e-05 8.463985e-05 8.529926e-05 8.595526e-05 8.660750e-05
## [55,] 8.289606e-05 8.358019e-05 8.426151e-05 8.493969e-05 8.561438e-05
## [56,] 8.180807e-05 8.251367e-05 8.321673e-05 8.391693e-05 8.461392e-05
## [57,] 8.071388e-05 8.144078e-05 8.216542e-05 8.288747e-05 8.360658e-05
## [58,] 7.961397e-05 8.036200e-05 8.110805e-05 8.185179e-05 8.259285e-05
## [59,] 7.850885e-05 7.927784e-05 8.004512e-05 8.081035e-05 8.157318e-05
## [60,] 7.739902e-05 7.818877e-05 7.897710e-05 7.976364e-05 8.054806e-05
## [61,] 7.628496e-05 7.709530e-05 7.790447e-05 7.871214e-05 7.951795e-05
## [62,] 7.516718e-05 7.599790e-05 7.682773e-05 7.765632e-05 7.848332e-05
## [63,] 7.404616e-05 7.489706e-05 7.574735e-05 7.659667e-05 7.744465e-05
## [64,] 7.292239e-05 7.379327e-05 7.466380e-05 7.553364e-05 7.640240e-05
## [65,] 7.179634e-05 7.268700e-05 7.357757e-05 7.446770e-05 7.535704e-05
## [66,] 7.066850e-05 7.157871e-05 7.248910e-05 7.339933e-05 7.430901e-05
## [67,] 6.953933e-05 7.046888e-05 7.139888e-05 7.232896e-05 7.325877e-05
## [68,] 6.840929e-05 6.935796e-05 7.030734e-05 7.125707e-05 7.220678e-05
## [69,] 6.727884e-05 6.824640e-05 6.921493e-05 7.018407e-05 7.115346e-05
## [70,] 6.614842e-05 6.713465e-05 6.812210e-05 6.911043e-05 7.009925e-05
## [71,] 6.501846e-05 6.602313e-05 6.702928e-05 6.803655e-05 6.904457e-05
## [72,] 6.388940e-05 6.491226e-05 6.593687e-05 6.696286e-05 6.798985e-05
## [73,] 6.276164e-05 6.380248e-05 6.484531e-05 6.588977e-05 6.693548e-05
## [74,] 6.163560e-05 6.269417e-05 6.375498e-05 6.481767e-05 6.588186e-05
## [75,] 6.051166e-05 6.158773e-05 6.266628e-05 6.374696e-05 6.482939e-05
## [76,] 5.939022e-05 6.048353e-05 6.157959e-05 6.267802e-05 6.377844e-05
## [77,] 5.827164e-05 5.938197e-05 6.049528e-05 6.161121e-05 6.272937e-05
## [78,] 5.715628e-05 5.828338e-05 5.941370e-05 6.054689e-05 6.168255e-05
## [79,] 5.604449e-05 5.718812e-05 5.833521e-05 5.948540e-05 6.063831e-05
## [80,] 5.493660e-05 5.609652e-05 5.726014e-05 5.842709e-05 5.959699e-05
## [81,] 5.383295e-05 5.500891e-05 5.618880e-05 5.737227e-05 5.855891e-05
## [82,] 5.273383e-05 5.392559e-05 5.512152e-05 5.632125e-05 5.752439e-05
## [83,] 5.163955e-05 5.284687e-05 5.405858e-05 5.527433e-05 5.649372e-05
## [84,] 5.055039e-05 5.177302e-05 5.300028e-05 5.423180e-05 5.546719e-05
## [85,] 4.946663e-05 5.070433e-05 5.194689e-05 5.319394e-05 5.444507e-05
## [86,] 4.838852e-05 4.964106e-05 5.089867e-05 5.216100e-05 5.342763e-05
## [87,] 4.731632e-05 4.858345e-05 4.985588e-05 5.113323e-05 5.241512e-05
## [88,] 4.625025e-05 4.753173e-05 4.881874e-05 5.011088e-05 5.140778e-05
## [89,] 4.519054e-05 4.648615e-05 4.778748e-05 4.909418e-05 5.040584e-05
## [90,] 4.413741e-05 4.544690e-05 4.676233e-05 4.808333e-05 4.940952e-05
## [91,] 4.309105e-05 4.441418e-05 4.574347e-05 4.707855e-05 4.841901e-05
## [92,] 4.205165e-05 4.338820e-05 4.473111e-05 4.608002e-05 4.743452e-05
## [93,] 4.101939e-05 4.236912e-05 4.372542e-05 4.508792e-05 4.645623e-05
## [94,] 3.999442e-05 4.135711e-05 4.272658e-05 4.410244e-05 4.548431e-05
## [95,] 3.897691e-05 4.035233e-05 4.173473e-05 4.312372e-05 4.451892e-05
## [96,] 3.796700e-05 3.935492e-05 4.075002e-05 4.215192e-05 4.356022e-05
## [97,] 3.696482e-05 3.836502e-05 3.977260e-05 4.118717e-05 4.260834e-05
## [98,] 3.597048e-05 3.738275e-05 3.880259e-05 4.022961e-05 4.166342e-05
## [99,] 3.498411e-05 3.640823e-05 3.784010e-05 3.927935e-05 4.072558e-05
## [100,] 3.400580e-05 3.544155e-05 3.688525e-05 3.833651e-05 3.979493e-05
## [,11] [,12] [,13] [,14] [,15]
## [1,] 1.200604e-04 1.194815e-04 1.188859e-04 1.182732e-04 1.176436e-04
## [2,] 1.198218e-04 1.192626e-04 1.186867e-04 1.180940e-04 1.174844e-04
## [3,] 1.195704e-04 1.190310e-04 1.184751e-04 1.179025e-04 1.173132e-04
## [4,] 1.193058e-04 1.187865e-04 1.182508e-04 1.176986e-04 1.171298e-04
## [5,] 1.190279e-04 1.185288e-04 1.180135e-04 1.174820e-04 1.169340e-04
## [6,] 1.187364e-04 1.182578e-04 1.177631e-04 1.172524e-04 1.167254e-04
## [7,] 1.184311e-04 1.179731e-04 1.174994e-04 1.170097e-04 1.165039e-04
## [8,] 1.181117e-04 1.176747e-04 1.172220e-04 1.167535e-04 1.162692e-04
## [9,] 1.177782e-04 1.173622e-04 1.169308e-04 1.164838e-04 1.160211e-04
## [10,] 1.174302e-04 1.170355e-04 1.166256e-04 1.162003e-04 1.157594e-04
## [11,] 1.170676e-04 1.166944e-04 1.163062e-04 1.159027e-04 1.154839e-04
## [12,] 1.166901e-04 1.163387e-04 1.159724e-04 1.155910e-04 1.151944e-04
## [13,] 1.162978e-04 1.159682e-04 1.156240e-04 1.152648e-04 1.148907e-04
## [14,] 1.158903e-04 1.155828e-04 1.152608e-04 1.149241e-04 1.145726e-04
## [15,] 1.154675e-04 1.151823e-04 1.148827e-04 1.145687e-04 1.142400e-04
## [16,] 1.150294e-04 1.147665e-04 1.144896e-04 1.141984e-04 1.138928e-04
## [17,] 1.145757e-04 1.143354e-04 1.140813e-04 1.138131e-04 1.135307e-04
## [18,] 1.141064e-04 1.138889e-04 1.136577e-04 1.134127e-04 1.131536e-04
## [19,] 1.136213e-04 1.134267e-04 1.132187e-04 1.129970e-04 1.127614e-04
## [20,] 1.131204e-04 1.129489e-04 1.127642e-04 1.125659e-04 1.123541e-04
## [21,] 1.126037e-04 1.124554e-04 1.122941e-04 1.121195e-04 1.119314e-04
## [22,] 1.120711e-04 1.119461e-04 1.118083e-04 1.116575e-04 1.114934e-04
## [23,] 1.115225e-04 1.114210e-04 1.113069e-04 1.111800e-04 1.110400e-04
## [24,] 1.109579e-04 1.108800e-04 1.107897e-04 1.106869e-04 1.105712e-04
## [25,] 1.103773e-04 1.103232e-04 1.102568e-04 1.101781e-04 1.100868e-04
## [26,] 1.097809e-04 1.097505e-04 1.097082e-04 1.096538e-04 1.095870e-04
## [27,] 1.091685e-04 1.091620e-04 1.091439e-04 1.091138e-04 1.090716e-04
## [28,] 1.085402e-04 1.085578e-04 1.085639e-04 1.085583e-04 1.085408e-04
## [29,] 1.078962e-04 1.079378e-04 1.079683e-04 1.079872e-04 1.079945e-04
## [30,] 1.072365e-04 1.073023e-04 1.073571e-04 1.074007e-04 1.074329e-04
## [31,] 1.065612e-04 1.066512e-04 1.067305e-04 1.067988e-04 1.068559e-04
## [32,] 1.058705e-04 1.059848e-04 1.060886e-04 1.061817e-04 1.062638e-04
## [33,] 1.051644e-04 1.053031e-04 1.054315e-04 1.055494e-04 1.056565e-04
## [34,] 1.044433e-04 1.046063e-04 1.047593e-04 1.049021e-04 1.050343e-04
## [35,] 1.037072e-04 1.038946e-04 1.040722e-04 1.042399e-04 1.043973e-04
## [36,] 1.029563e-04 1.031681e-04 1.033705e-04 1.035631e-04 1.037456e-04
## [37,] 1.021910e-04 1.024272e-04 1.026542e-04 1.028717e-04 1.030794e-04
## [38,] 1.014113e-04 1.016720e-04 1.019237e-04 1.021661e-04 1.023990e-04
## [39,] 1.006177e-04 1.009028e-04 1.011792e-04 1.014465e-04 1.017045e-04
## [40,] 9.981034e-05 1.001198e-04 1.004208e-04 1.007131e-04 1.009963e-04
## [41,] 9.898952e-05 9.932338e-05 9.964901e-05 9.996614e-05 1.002744e-04
## [42,] 9.815558e-05 9.851376e-05 9.886398e-05 9.920594e-05 9.953933e-05
## [43,] 9.730882e-05 9.769128e-05 9.806604e-05 9.843279e-05 9.879123e-05
## [44,] 9.644959e-05 9.685627e-05 9.725551e-05 9.764701e-05 9.803043e-05
## [45,] 9.557825e-05 9.600908e-05 9.643274e-05 9.684891e-05 9.725725e-05
## [46,] 9.469516e-05 9.515007e-05 9.559807e-05 9.603883e-05 9.647203e-05
## [47,] 9.380071e-05 9.427961e-05 9.475186e-05 9.521714e-05 9.567510e-05
## [48,] 9.289529e-05 9.339808e-05 9.389449e-05 9.438418e-05 9.486682e-05
## [49,] 9.197930e-05 9.250588e-05 9.302635e-05 9.354035e-05 9.404756e-05
## [50,] 9.105315e-05 9.160342e-05 9.214783e-05 9.268603e-05 9.321770e-05
## [51,] 9.011728e-05 9.069110e-05 9.125933e-05 9.182162e-05 9.237763e-05
## [52,] 8.917210e-05 8.976936e-05 9.036128e-05 9.094752e-05 9.152774e-05
## [53,] 8.821807e-05 8.883862e-05 8.945409e-05 9.006415e-05 9.066844e-05
## [54,] 8.725563e-05 8.789932e-05 8.853821e-05 8.917193e-05 8.980014e-05
## [55,] 8.628524e-05 8.695191e-05 8.761405e-05 8.827129e-05 8.892328e-05
## [56,] 8.530734e-05 8.599685e-05 8.668208e-05 8.736267e-05 8.803826e-05
## [57,] 8.432240e-05 8.503457e-05 8.574272e-05 8.644650e-05 8.714553e-05
## [58,] 8.333088e-05 8.406554e-05 8.479644e-05 8.552322e-05 8.624552e-05
## [59,] 8.233326e-05 8.309021e-05 8.384368e-05 8.459329e-05 8.533866e-05
## [60,] 8.132998e-05 8.210905e-05 8.288490e-05 8.365714e-05 8.442540e-05
## [61,] 8.032153e-05 8.112252e-05 8.192055e-05 8.271523e-05 8.350618e-05
## [62,] 7.930837e-05 8.013108e-05 8.095108e-05 8.176800e-05 8.258144e-05
## [63,] 7.829095e-05 7.913517e-05 7.997695e-05 8.081590e-05 8.165162e-05
## [64,] 7.726974e-05 7.813527e-05 7.899861e-05 7.985937e-05 8.071715e-05
## [65,] 7.624520e-05 7.713182e-05 7.801650e-05 7.889886e-05 7.977849e-05
## [66,] 7.521778e-05 7.612527e-05 7.703107e-05 7.793480e-05 7.883605e-05
## [67,] 7.418793e-05 7.511606e-05 7.604276e-05 7.696763e-05 7.789028e-05
## [68,] 7.315609e-05 7.410463e-05 7.505200e-05 7.599779e-05 7.694160e-05
## [69,] 7.212270e-05 7.309142e-05 7.405922e-05 7.502569e-05 7.599042e-05
## [70,] 7.108818e-05 7.207685e-05 7.306484e-05 7.405175e-05 7.503716e-05
## [71,] 7.005296e-05 7.106133e-05 7.206927e-05 7.307638e-05 7.408224e-05
## [72,] 6.901745e-05 7.004528e-05 7.107294e-05 7.210000e-05 7.312605e-05
## [73,] 6.798206e-05 6.902911e-05 7.007622e-05 7.112299e-05 7.216899e-05
## [74,] 6.694717e-05 6.801319e-05 6.907953e-05 7.014575e-05 7.121144e-05
## [75,] 6.591318e-05 6.699793e-05 6.808322e-05 6.916865e-05 7.025378e-05
## [76,] 6.488046e-05 6.598368e-05 6.708769e-05 6.819207e-05 6.929638e-05
## [77,] 6.384938e-05 6.497082e-05 6.609329e-05 6.721636e-05 6.833960e-05
## [78,] 6.282029e-05 6.395970e-05 6.510038e-05 6.624189e-05 6.738379e-05
## [79,] 6.179353e-05 6.295066e-05 6.410929e-05 6.526898e-05 6.642930e-05
## [80,] 6.076944e-05 6.194404e-05 6.312036e-05 6.429798e-05 6.547644e-05
## [81,] 5.974835e-05 6.094015e-05 6.213391e-05 6.332919e-05 6.452555e-05
## [82,] 5.873055e-05 5.993931e-05 6.115026e-05 6.236294e-05 6.357693e-05
## [83,] 5.771636e-05 5.894182e-05 6.016969e-05 6.139952e-05 6.263087e-05
## [84,] 5.670605e-05 5.794796e-05 5.919250e-05 6.043922e-05 6.168768e-05
## [85,] 5.569990e-05 5.695801e-05 5.821896e-05 5.948232e-05 6.074763e-05
## [86,] 5.469818e-05 5.597223e-05 5.724934e-05 5.852907e-05 5.981097e-05
## [87,] 5.370115e-05 5.499088e-05 5.628390e-05 5.757975e-05 5.887798e-05
## [88,] 5.270903e-05 5.401421e-05 5.532287e-05 5.663459e-05 5.794890e-05
## [89,] 5.172207e-05 5.304243e-05 5.436650e-05 5.569383e-05 5.702395e-05
## [90,] 5.074047e-05 5.207578e-05 5.341500e-05 5.475768e-05 5.610337e-05
## [91,] 4.976445e-05 5.111445e-05 5.246858e-05 5.382637e-05 5.518736e-05
## [92,] 4.879421e-05 5.015866e-05 5.152744e-05 5.290009e-05 5.427614e-05
## [93,] 4.782992e-05 4.920858e-05 5.059177e-05 5.197903e-05 5.336989e-05
## [94,] 4.687177e-05 4.826439e-05 4.966175e-05 5.106337e-05 5.246880e-05
## [95,] 4.591991e-05 4.732627e-05 4.873755e-05 5.015329e-05 5.157304e-05
## [96,] 4.497450e-05 4.639435e-05 4.781932e-05 4.924895e-05 5.068276e-05
## [97,] 4.403569e-05 4.546880e-05 4.690722e-05 4.835049e-05 4.979813e-05
## [98,] 4.310361e-05 4.454974e-05 4.600138e-05 4.745805e-05 4.891929e-05
## [99,] 4.217838e-05 4.363731e-05 4.510193e-05 4.657178e-05 4.804637e-05
## [100,] 4.126011e-05 4.273161e-05 4.420899e-05 4.569178e-05 4.717950e-05
## [,16] [,17] [,18] [,19] [,20]
## [1,] 1.169968e-04 1.163327e-04 1.156514e-04 1.149528e-04 1.142369e-04
## [2,] 1.168578e-04 1.162142e-04 1.155534e-04 1.148754e-04 1.141802e-04
## [3,] 1.167071e-04 1.160841e-04 1.154440e-04 1.147869e-04 1.141128e-04
## [4,] 1.165444e-04 1.159422e-04 1.153231e-04 1.146872e-04 1.140342e-04
## [5,] 1.163695e-04 1.157883e-04 1.151905e-04 1.145758e-04 1.139444e-04
## [6,] 1.161820e-04 1.156222e-04 1.150458e-04 1.144527e-04 1.138430e-04
## [7,] 1.159819e-04 1.154435e-04 1.148888e-04 1.143176e-04 1.137299e-04
## [8,] 1.157687e-04 1.152522e-04 1.147193e-04 1.141702e-04 1.136046e-04
## [9,] 1.155425e-04 1.150478e-04 1.145371e-04 1.140103e-04 1.134671e-04
## [10,] 1.153028e-04 1.148303e-04 1.143420e-04 1.138376e-04 1.133171e-04
## [11,] 1.150495e-04 1.145995e-04 1.141337e-04 1.136520e-04 1.131544e-04
## [12,] 1.147824e-04 1.143550e-04 1.139120e-04 1.134532e-04 1.129787e-04
## [13,] 1.145014e-04 1.140967e-04 1.136767e-04 1.132411e-04 1.127898e-04
## [14,] 1.142061e-04 1.138245e-04 1.134276e-04 1.130154e-04 1.125876e-04
## [15,] 1.138966e-04 1.135381e-04 1.131646e-04 1.127759e-04 1.123718e-04
## [16,] 1.135725e-04 1.132375e-04 1.128875e-04 1.125225e-04 1.121423e-04
## [17,] 1.132338e-04 1.129223e-04 1.125961e-04 1.122550e-04 1.118989e-04
## [18,] 1.128802e-04 1.125925e-04 1.122902e-04 1.119733e-04 1.116415e-04
## [19,] 1.125118e-04 1.122480e-04 1.119698e-04 1.116771e-04 1.113698e-04
## [20,] 1.121284e-04 1.118886e-04 1.116347e-04 1.113665e-04 1.110837e-04
## [21,] 1.117298e-04 1.115143e-04 1.112848e-04 1.110412e-04 1.107832e-04
## [22,] 1.113160e-04 1.111249e-04 1.109200e-04 1.107011e-04 1.104681e-04
## [23,] 1.108869e-04 1.107203e-04 1.105402e-04 1.103462e-04 1.101383e-04
## [24,] 1.104425e-04 1.103006e-04 1.101453e-04 1.099764e-04 1.097938e-04
## [25,] 1.099827e-04 1.098656e-04 1.097353e-04 1.095916e-04 1.094344e-04
## [26,] 1.095076e-04 1.094154e-04 1.093102e-04 1.091918e-04 1.090601e-04
## [27,] 1.090171e-04 1.089499e-04 1.088699e-04 1.087770e-04 1.086709e-04
## [28,] 1.085111e-04 1.084691e-04 1.084145e-04 1.083471e-04 1.082667e-04
## [29,] 1.079899e-04 1.079731e-04 1.079439e-04 1.079021e-04 1.078476e-04
## [30,] 1.074533e-04 1.074618e-04 1.074582e-04 1.074421e-04 1.074135e-04
## [31,] 1.069015e-04 1.069354e-04 1.069574e-04 1.069671e-04 1.069645e-04
## [32,] 1.063346e-04 1.063940e-04 1.064416e-04 1.064772e-04 1.065006e-04
## [33,] 1.057526e-04 1.058375e-04 1.059108e-04 1.059724e-04 1.060220e-04
## [34,] 1.051558e-04 1.052662e-04 1.053653e-04 1.054528e-04 1.055286e-04
## [35,] 1.045441e-04 1.046801e-04 1.048050e-04 1.049186e-04 1.050206e-04
## [36,] 1.039178e-04 1.040794e-04 1.042301e-04 1.043698e-04 1.044981e-04
## [37,] 1.032770e-04 1.034643e-04 1.036409e-04 1.038066e-04 1.039612e-04
## [38,] 1.026220e-04 1.028349e-04 1.030374e-04 1.032292e-04 1.034101e-04
## [39,] 1.019530e-04 1.021915e-04 1.024199e-04 1.026378e-04 1.028450e-04
## [40,] 1.012701e-04 1.015342e-04 1.017885e-04 1.020325e-04 1.022660e-04
## [41,] 1.005736e-04 1.008634e-04 1.011435e-04 1.014135e-04 1.016733e-04
## [42,] 9.986385e-05 1.001792e-04 1.004851e-04 1.007812e-04 1.010672e-04
## [43,] 9.914104e-05 9.948191e-05 9.981355e-05 1.001357e-04 1.004479e-04
## [44,] 9.840548e-05 9.877183e-05 9.912918e-05 9.947723e-05 9.981567e-05
## [45,] 9.765747e-05 9.804924e-05 9.843225e-05 9.880618e-05 9.917073e-05
## [46,] 9.689735e-05 9.731446e-05 9.772304e-05 9.812279e-05 9.851337e-05
## [47,] 9.612543e-05 9.656780e-05 9.700189e-05 9.742736e-05 9.784391e-05
## [48,] 9.534208e-05 9.580962e-05 9.626911e-05 9.672022e-05 9.716264e-05
## [49,] 9.454764e-05 9.504025e-05 9.552504e-05 9.600170e-05 9.646988e-05
## [50,] 9.374249e-05 9.426005e-05 9.477004e-05 9.527213e-05 9.576597e-05
## [51,] 9.292700e-05 9.346940e-05 9.400447e-05 9.453187e-05 9.505126e-05
## [52,] 9.210157e-05 9.266868e-05 9.322870e-05 9.378128e-05 9.432608e-05
## [53,] 9.126659e-05 9.185827e-05 9.244310e-05 9.302073e-05 9.359081e-05
## [54,] 9.042248e-05 9.103857e-05 9.164807e-05 9.225061e-05 9.284582e-05
## [55,] 8.956963e-05 9.021000e-05 9.084401e-05 9.147129e-05 9.209148e-05
## [56,] 8.870848e-05 8.937295e-05 9.003131e-05 9.068318e-05 9.132818e-05
## [57,] 8.783944e-05 8.852785e-05 8.921038e-05 8.988667e-05 9.055632e-05
## [58,] 8.696294e-05 8.767511e-05 8.838164e-05 8.908217e-05 8.977629e-05
## [59,] 8.607941e-05 8.681516e-05 8.754551e-05 8.827009e-05 8.898849e-05
## [60,] 8.518929e-05 8.594842e-05 8.670240e-05 8.745083e-05 8.819333e-05
## [61,] 8.429301e-05 8.507532e-05 8.585273e-05 8.662483e-05 8.739122e-05
## [62,] 8.339100e-05 8.419630e-05 8.499693e-05 8.579248e-05 8.658256e-05
## [63,] 8.248371e-05 8.331178e-05 8.413542e-05 8.495422e-05 8.576777e-05
## [64,] 8.157156e-05 8.242219e-05 8.326862e-05 8.411045e-05 8.494725e-05
## [65,] 8.065499e-05 8.152795e-05 8.239695e-05 8.326159e-05 8.412143e-05
## [66,] 7.973442e-05 8.062949e-05 8.152084e-05 8.240805e-05 8.329070e-05
## [67,] 7.881029e-05 7.972723e-05 8.064070e-05 8.155025e-05 8.245547e-05
## [68,] 7.788300e-05 7.882159e-05 7.975694e-05 8.068860e-05 8.161615e-05
## [69,] 7.695299e-05 7.791298e-05 7.886996e-05 7.982349e-05 8.077313e-05
## [70,] 7.602066e-05 7.700181e-05 7.798019e-05 7.895534e-05 7.992682e-05
## [71,] 7.508642e-05 7.608848e-05 7.708800e-05 7.808453e-05 7.907760e-05
## [72,] 7.415066e-05 7.517339e-05 7.619380e-05 7.721145e-05 7.822587e-05
## [73,] 7.321377e-05 7.425692e-05 7.529797e-05 7.633648e-05 7.737199e-05
## [74,] 7.227615e-05 7.333946e-05 7.440089e-05 7.546001e-05 7.651634e-05
## [75,] 7.133817e-05 7.242137e-05 7.350294e-05 7.458240e-05 7.565930e-05
## [76,] 7.040018e-05 7.150303e-05 7.260446e-05 7.370401e-05 7.480121e-05
## [77,] 6.946256e-05 7.058479e-05 7.170583e-05 7.282520e-05 7.394244e-05
## [78,] 6.852565e-05 6.966700e-05 7.080738e-05 7.194631e-05 7.308332e-05
## [79,] 6.758979e-05 6.875000e-05 6.990945e-05 7.106768e-05 7.222419e-05
## [80,] 6.665531e-05 6.783411e-05 6.901237e-05 7.018962e-05 7.136537e-05
## [81,] 6.572253e-05 6.691966e-05 6.811647e-05 6.931248e-05 7.050719e-05
## [82,] 6.479175e-05 6.600695e-05 6.722204e-05 6.843654e-05 6.964995e-05
## [83,] 6.386329e-05 6.509628e-05 6.632939e-05 6.756211e-05 6.879395e-05
## [84,] 6.293742e-05 6.418795e-05 6.543880e-05 6.668948e-05 6.793948e-05
## [85,] 6.201442e-05 6.328223e-05 6.455057e-05 6.581893e-05 6.708681e-05
## [86,] 6.109457e-05 6.237939e-05 6.366494e-05 6.495072e-05 6.623623e-05
## [87,] 6.017812e-05 6.147969e-05 6.278219e-05 6.408513e-05 6.538798e-05
## [88,] 5.926532e-05 6.058337e-05 6.190256e-05 6.322238e-05 6.454232e-05
## [89,] 5.835639e-05 5.969067e-05 6.102629e-05 6.236274e-05 6.369950e-05
## [90,] 5.745158e-05 5.880183e-05 6.015361e-05 6.150642e-05 6.285973e-05
## [91,] 5.655109e-05 5.791704e-05 5.928474e-05 6.065364e-05 6.202324e-05
## [92,] 5.565512e-05 5.703653e-05 5.841987e-05 5.980462e-05 6.119025e-05
## [93,] 5.476388e-05 5.616049e-05 5.755922e-05 5.895955e-05 6.036095e-05
## [94,] 5.387754e-05 5.528910e-05 5.670298e-05 5.811863e-05 5.953554e-05
## [95,] 5.299629e-05 5.442255e-05 5.585131e-05 5.728203e-05 5.871420e-05
## [96,] 5.212028e-05 5.356099e-05 5.500438e-05 5.644993e-05 5.789710e-05
## [97,] 5.124967e-05 5.270459e-05 5.416237e-05 5.562249e-05 5.708441e-05
## [98,] 5.038461e-05 5.185349e-05 5.332542e-05 5.479986e-05 5.627628e-05
## [99,] 4.952523e-05 5.100783e-05 5.249366e-05 5.398219e-05 5.547286e-05
## [100,] 4.867166e-05 5.016775e-05 5.166724e-05 5.316960e-05 5.467428e-05
## [,21] [,22] [,23] [,24] [,25]
## [1,] 1.135036e-04 1.127530e-04 1.119851e-04 1.112000e-04 1.103977e-04
## [2,] 1.134678e-04 1.127382e-04 1.119914e-04 1.112275e-04 1.104465e-04
## [3,] 1.134215e-04 1.127131e-04 1.119877e-04 1.112452e-04 1.104858e-04
## [4,] 1.133644e-04 1.126775e-04 1.119737e-04 1.112529e-04 1.105153e-04
## [5,] 1.132961e-04 1.126310e-04 1.119490e-04 1.112502e-04 1.105346e-04
## [6,] 1.132166e-04 1.125735e-04 1.119136e-04 1.112370e-04 1.105437e-04
## [7,] 1.131255e-04 1.125046e-04 1.118670e-04 1.112129e-04 1.105422e-04
## [8,] 1.130226e-04 1.124241e-04 1.118092e-04 1.111777e-04 1.105298e-04
## [9,] 1.129077e-04 1.123319e-04 1.117397e-04 1.111312e-04 1.105063e-04
## [10,] 1.127804e-04 1.122276e-04 1.116585e-04 1.110731e-04 1.104715e-04
## [11,] 1.126407e-04 1.121110e-04 1.115651e-04 1.110032e-04 1.104251e-04
## [12,] 1.124882e-04 1.119819e-04 1.114595e-04 1.109212e-04 1.103668e-04
## [13,] 1.123228e-04 1.118400e-04 1.113414e-04 1.108269e-04 1.102965e-04
## [14,] 1.121442e-04 1.116853e-04 1.112106e-04 1.107201e-04 1.102139e-04
## [15,] 1.119523e-04 1.115174e-04 1.110668e-04 1.106006e-04 1.101188e-04
## [16,] 1.117469e-04 1.113361e-04 1.109099e-04 1.104682e-04 1.100110e-04
## [17,] 1.115277e-04 1.111414e-04 1.107397e-04 1.103227e-04 1.098903e-04
## [18,] 1.112947e-04 1.109329e-04 1.105560e-04 1.101639e-04 1.097565e-04
## [19,] 1.110477e-04 1.107106e-04 1.103586e-04 1.099916e-04 1.096094e-04
## [20,] 1.107864e-04 1.104743e-04 1.101475e-04 1.098057e-04 1.094489e-04
## [21,] 1.105109e-04 1.102239e-04 1.099223e-04 1.096059e-04 1.092747e-04
## [22,] 1.102209e-04 1.099592e-04 1.096831e-04 1.093923e-04 1.090868e-04
## [23,] 1.099164e-04 1.096802e-04 1.094296e-04 1.091646e-04 1.088850e-04
## [24,] 1.095972e-04 1.093866e-04 1.091618e-04 1.089227e-04 1.086692e-04
## [25,] 1.092634e-04 1.090785e-04 1.088796e-04 1.086665e-04 1.084392e-04
## [26,] 1.089148e-04 1.087558e-04 1.085829e-04 1.083960e-04 1.081950e-04
## [27,] 1.085514e-04 1.084183e-04 1.082716e-04 1.081111e-04 1.079366e-04
## [28,] 1.081731e-04 1.080662e-04 1.079457e-04 1.078116e-04 1.076637e-04
## [29,] 1.077800e-04 1.076993e-04 1.076052e-04 1.074977e-04 1.073764e-04
## [30,] 1.073720e-04 1.073176e-04 1.072500e-04 1.071691e-04 1.070747e-04
## [31,] 1.069493e-04 1.069212e-04 1.068802e-04 1.068260e-04 1.067586e-04
## [32,] 1.065117e-04 1.065101e-04 1.064958e-04 1.064684e-04 1.064279e-04
## [33,] 1.060594e-04 1.060843e-04 1.060967e-04 1.060962e-04 1.060828e-04
## [34,] 1.055924e-04 1.056439e-04 1.056831e-04 1.057096e-04 1.057233e-04
## [35,] 1.051108e-04 1.051890e-04 1.052550e-04 1.053085e-04 1.053493e-04
## [36,] 1.046148e-04 1.047197e-04 1.048125e-04 1.048930e-04 1.049611e-04
## [37,] 1.041044e-04 1.042360e-04 1.043557e-04 1.044633e-04 1.045587e-04
## [38,] 1.035799e-04 1.037382e-04 1.038848e-04 1.040195e-04 1.041421e-04
## [39,] 1.030412e-04 1.032263e-04 1.033998e-04 1.035616e-04 1.037115e-04
## [40,] 1.024888e-04 1.027005e-04 1.029009e-04 1.030899e-04 1.032670e-04
## [41,] 1.019226e-04 1.021610e-04 1.023884e-04 1.026044e-04 1.028088e-04
## [42,] 1.013430e-04 1.016081e-04 1.018623e-04 1.021054e-04 1.023371e-04
## [43,] 1.007501e-04 1.010418e-04 1.013229e-04 1.015930e-04 1.018520e-04
## [44,] 1.001442e-04 1.004626e-04 1.007704e-04 1.010675e-04 1.013536e-04
## [45,] 9.952559e-05 9.987047e-05 1.002051e-04 1.005291e-04 1.008424e-04
## [46,] 9.889450e-05 9.926585e-05 9.962713e-05 9.997806e-05 1.003183e-04
## [47,] 9.825121e-05 9.864895e-05 9.903683e-05 9.941455e-05 9.978182e-05
## [48,] 9.759603e-05 9.802008e-05 9.843447e-05 9.883890e-05 9.923306e-05
## [49,] 9.692926e-05 9.737952e-05 9.782032e-05 9.825137e-05 9.867234e-05
## [50,] 9.625124e-05 9.672759e-05 9.719470e-05 9.765225e-05 9.809993e-05
## [51,] 9.556228e-05 9.606462e-05 9.655792e-05 9.704186e-05 9.751612e-05
## [52,] 9.486275e-05 9.539093e-05 9.591030e-05 9.642051e-05 9.692124e-05
## [53,] 9.415298e-05 9.470689e-05 9.525218e-05 9.578853e-05 9.631558e-05
## [54,] 9.343334e-05 9.401282e-05 9.458391e-05 9.514624e-05 9.569948e-05
## [55,] 9.270421e-05 9.330911e-05 9.390583e-05 9.449400e-05 9.507327e-05
## [56,] 9.196595e-05 9.259612e-05 9.321831e-05 9.383215e-05 9.443730e-05
## [57,] 9.121896e-05 9.187422e-05 9.252171e-05 9.316106e-05 9.379191e-05
## [58,] 9.046362e-05 9.114379e-05 9.181641e-05 9.248109e-05 9.313747e-05
## [59,] 8.970033e-05 9.040523e-05 9.110279e-05 9.179262e-05 9.247434e-05
## [60,] 8.892949e-05 8.965892e-05 9.038122e-05 9.109601e-05 9.180288e-05
## [61,] 8.815149e-05 8.890526e-05 8.965211e-05 9.039164e-05 9.112347e-05
## [62,] 8.736675e-05 8.814464e-05 8.891583e-05 8.967991e-05 9.043648e-05
## [63,] 8.657565e-05 8.737746e-05 8.817278e-05 8.896119e-05 8.974229e-05
## [64,] 8.577862e-05 8.660413e-05 8.742335e-05 8.823588e-05 8.904129e-05
## [65,] 8.497605e-05 8.582503e-05 8.666794e-05 8.750435e-05 8.833385e-05
## [66,] 8.416834e-05 8.504057e-05 8.590693e-05 8.676700e-05 8.762035e-05
## [67,] 8.335591e-05 8.425114e-05 8.514072e-05 8.602421e-05 8.690118e-05
## [68,] 8.253914e-05 8.345714e-05 8.436970e-05 8.527637e-05 8.617671e-05
## [69,] 8.171844e-05 8.265896e-05 8.359425e-05 8.452386e-05 8.544733e-05
## [70,] 8.089419e-05 8.185699e-05 8.281476e-05 8.376705e-05 8.471341e-05
## [71,] 8.006678e-05 8.105161e-05 8.203161e-05 8.300634e-05 8.397532e-05
## [72,] 7.923660e-05 8.024320e-05 8.124518e-05 8.224208e-05 8.323343e-05
## [73,] 7.840403e-05 7.943213e-05 8.045583e-05 8.147464e-05 8.248810e-05
## [74,] 7.756942e-05 7.861878e-05 7.966393e-05 8.070439e-05 8.173970e-05
## [75,] 7.673316e-05 7.780350e-05 7.886983e-05 7.993169e-05 8.098857e-05
## [76,] 7.589559e-05 7.698665e-05 7.807391e-05 7.915688e-05 8.023507e-05
## [77,] 7.505706e-05 7.616857e-05 7.727649e-05 7.838031e-05 7.947954e-05
## [78,] 7.421792e-05 7.534962e-05 7.647791e-05 7.760231e-05 7.872231e-05
## [79,] 7.337850e-05 7.453011e-05 7.567852e-05 7.682322e-05 7.796371e-05
## [80,] 7.253912e-05 7.371038e-05 7.487863e-05 7.604336e-05 7.720406e-05
## [81,] 7.170011e-05 7.289074e-05 7.407855e-05 7.526304e-05 7.644368e-05
## [82,] 7.086177e-05 7.207149e-05 7.327860e-05 7.448256e-05 7.568287e-05
## [83,] 7.002440e-05 7.125294e-05 7.247906e-05 7.370224e-05 7.492193e-05
## [84,] 6.918828e-05 7.043538e-05 7.168024e-05 7.292235e-05 7.416115e-05
## [85,] 6.835370e-05 6.961908e-05 7.088241e-05 7.214317e-05 7.340081e-05
## [86,] 6.752093e-05 6.880432e-05 7.008585e-05 7.136498e-05 7.264117e-05
## [87,] 6.669023e-05 6.799135e-05 6.929080e-05 7.058804e-05 7.188252e-05
## [88,] 6.586185e-05 6.718044e-05 6.849754e-05 6.981261e-05 7.112509e-05
## [89,] 6.503603e-05 6.637182e-05 6.770629e-05 6.903892e-05 7.036913e-05
## [90,] 6.421301e-05 6.556572e-05 6.691731e-05 6.826722e-05 6.961489e-05
## [91,] 6.339300e-05 6.476237e-05 6.613080e-05 6.749773e-05 6.886259e-05
## [92,] 6.257622e-05 6.396199e-05 6.534699e-05 6.673067e-05 6.811244e-05
## [93,] 6.176288e-05 6.316477e-05 6.456609e-05 6.596624e-05 6.736467e-05
## [94,] 6.095316e-05 6.237093e-05 6.378828e-05 6.520466e-05 6.661947e-05
## [95,] 6.014725e-05 6.158063e-05 6.301377e-05 6.444610e-05 6.587702e-05
## [96,] 5.934533e-05 6.079406e-05 6.224273e-05 6.369075e-05 6.513753e-05
## [97,] 5.854756e-05 6.001140e-05 6.147533e-05 6.293878e-05 6.440116e-05
## [98,] 5.775411e-05 5.923279e-05 6.071174e-05 6.219037e-05 6.366808e-05
## [99,] 5.696512e-05 5.845839e-05 5.995210e-05 6.144565e-05 6.293845e-05
## [100,] 5.618072e-05 5.768835e-05 5.919657e-05 6.070480e-05 6.221243e-05
## [,26] [,27] [,28] [,29] [,30]
## [1,] 1.095783e-04 1.087419e-04 1.078888e-04 1.070189e-04 1.061326e-04
## [2,] 1.096485e-04 1.088336e-04 1.080020e-04 1.071538e-04 1.062891e-04
## [3,] 1.097094e-04 1.089163e-04 1.081064e-04 1.072801e-04 1.064373e-04
## [4,] 1.097608e-04 1.089896e-04 1.082018e-04 1.073976e-04 1.065770e-04
## [5,] 1.098023e-04 1.090534e-04 1.082879e-04 1.075060e-04 1.067079e-04
## [6,] 1.098338e-04 1.091074e-04 1.083645e-04 1.076052e-04 1.068298e-04
## [7,] 1.098549e-04 1.091512e-04 1.084311e-04 1.076948e-04 1.069423e-04
## [8,] 1.098654e-04 1.091847e-04 1.084877e-04 1.077745e-04 1.070452e-04
## [9,] 1.098651e-04 1.092076e-04 1.085339e-04 1.078441e-04 1.071383e-04
## [10,] 1.098536e-04 1.092196e-04 1.085695e-04 1.079033e-04 1.072212e-04
## [11,] 1.098308e-04 1.092205e-04 1.085942e-04 1.079519e-04 1.072938e-04
## [12,] 1.097964e-04 1.092101e-04 1.086078e-04 1.079897e-04 1.073557e-04
## [13,] 1.097502e-04 1.091880e-04 1.086100e-04 1.080162e-04 1.074067e-04
## [14,] 1.096919e-04 1.091541e-04 1.086006e-04 1.080314e-04 1.074466e-04
## [15,] 1.096213e-04 1.091082e-04 1.085794e-04 1.080350e-04 1.074751e-04
## [16,] 1.095383e-04 1.090500e-04 1.085461e-04 1.080268e-04 1.074920e-04
## [17,] 1.094425e-04 1.089792e-04 1.085006e-04 1.080064e-04 1.074970e-04
## [18,] 1.093338e-04 1.088958e-04 1.084425e-04 1.079738e-04 1.074899e-04
## [19,] 1.092121e-04 1.087995e-04 1.083717e-04 1.079287e-04 1.074705e-04
## [20,] 1.090770e-04 1.086901e-04 1.082881e-04 1.078709e-04 1.074387e-04
## [21,] 1.089286e-04 1.085675e-04 1.081914e-04 1.078003e-04 1.073942e-04
## [22,] 1.087665e-04 1.084314e-04 1.080815e-04 1.077166e-04 1.073368e-04
## [23,] 1.085908e-04 1.082818e-04 1.079581e-04 1.076196e-04 1.072663e-04
## [24,] 1.084011e-04 1.081185e-04 1.078213e-04 1.075093e-04 1.071827e-04
## [25,] 1.081975e-04 1.079414e-04 1.076707e-04 1.073855e-04 1.070857e-04
## [26,] 1.079798e-04 1.077503e-04 1.075064e-04 1.072481e-04 1.069752e-04
## [27,] 1.077480e-04 1.075452e-04 1.073282e-04 1.070968e-04 1.068511e-04
## [28,] 1.075019e-04 1.073260e-04 1.071360e-04 1.069318e-04 1.067133e-04
## [29,] 1.072415e-04 1.070926e-04 1.069297e-04 1.067527e-04 1.065616e-04
## [30,] 1.069667e-04 1.068449e-04 1.067093e-04 1.065597e-04 1.063961e-04
## [31,] 1.066776e-04 1.065830e-04 1.064747e-04 1.063526e-04 1.062165e-04
## [32,] 1.063741e-04 1.063068e-04 1.062259e-04 1.061314e-04 1.060230e-04
## [33,] 1.060562e-04 1.060163e-04 1.059629e-04 1.058960e-04 1.058154e-04
## [34,] 1.057239e-04 1.057115e-04 1.056857e-04 1.056465e-04 1.055937e-04
## [35,] 1.053774e-04 1.053924e-04 1.053943e-04 1.053828e-04 1.053579e-04
## [36,] 1.050165e-04 1.050591e-04 1.050886e-04 1.051050e-04 1.051081e-04
## [37,] 1.046415e-04 1.047116e-04 1.047689e-04 1.048132e-04 1.048442e-04
## [38,] 1.042524e-04 1.043501e-04 1.044351e-04 1.045073e-04 1.045663e-04
## [39,] 1.038492e-04 1.039746e-04 1.040874e-04 1.041874e-04 1.042745e-04
## [40,] 1.034322e-04 1.035852e-04 1.037258e-04 1.038537e-04 1.039689e-04
## [41,] 1.030015e-04 1.031821e-04 1.033504e-04 1.035063e-04 1.036495e-04
## [42,] 1.025571e-04 1.027653e-04 1.029614e-04 1.031452e-04 1.033165e-04
## [43,] 1.020994e-04 1.023352e-04 1.025590e-04 1.027706e-04 1.029699e-04
## [44,] 1.016284e-04 1.018917e-04 1.021432e-04 1.023827e-04 1.026100e-04
## [45,] 1.011445e-04 1.014352e-04 1.017143e-04 1.019816e-04 1.022368e-04
## [46,] 1.006477e-04 1.009658e-04 1.012726e-04 1.015676e-04 1.018506e-04
## [47,] 1.001383e-04 1.004838e-04 1.008181e-04 1.011407e-04 1.014516e-04
## [48,] 9.961666e-05 9.998943e-05 1.003511e-04 1.007013e-04 1.010399e-04
## [49,] 9.908293e-05 9.948286e-05 9.987183e-05 1.002496e-04 1.006158e-04
## [50,] 9.853741e-05 9.896440e-05 9.938060e-05 9.978574e-05 1.001795e-04
## [51,] 9.798038e-05 9.843432e-05 9.887765e-05 9.931006e-05 9.973127e-05
## [52,] 9.741214e-05 9.789291e-05 9.836324e-05 9.882281e-05 9.927134e-05
## [53,] 9.683300e-05 9.734047e-05 9.783766e-05 9.832426e-05 9.879997e-05
## [54,] 9.624328e-05 9.677730e-05 9.730122e-05 9.781471e-05 9.831747e-05
## [55,] 9.564329e-05 9.620372e-05 9.675422e-05 9.729445e-05 9.782410e-05
## [56,] 9.503339e-05 9.562006e-05 9.619697e-05 9.676379e-05 9.732018e-05
## [57,] 9.441389e-05 9.502664e-05 9.562981e-05 9.622304e-05 9.680600e-05
## [58,] 9.378517e-05 9.442382e-05 9.505306e-05 9.567253e-05 9.628189e-05
## [59,] 9.314757e-05 9.381194e-05 9.446707e-05 9.511260e-05 9.574817e-05
## [60,] 9.250145e-05 9.319134e-05 9.387217e-05 9.454357e-05 9.520517e-05
## [61,] 9.184718e-05 9.256240e-05 9.326873e-05 9.396579e-05 9.465322e-05
## [62,] 9.118513e-05 9.192546e-05 9.265709e-05 9.337961e-05 9.409266e-05
## [63,] 9.051566e-05 9.128090e-05 9.203761e-05 9.278538e-05 9.352384e-05
## [64,] 8.983916e-05 9.062909e-05 9.141065e-05 9.218346e-05 9.294710e-05
## [65,] 8.915600e-05 8.997038e-05 9.077658e-05 9.157419e-05 9.236280e-05
## [66,] 8.846654e-05 8.930516e-05 9.013577e-05 9.095795e-05 9.177128e-05
## [67,] 8.777118e-05 8.863379e-05 8.948856e-05 9.033508e-05 9.117291e-05
## [68,] 8.707028e-05 8.795664e-05 8.883534e-05 8.970595e-05 9.056803e-05
## [69,] 8.636422e-05 8.727408e-05 8.817646e-05 8.907091e-05 8.995700e-05
## [70,] 8.565337e-05 8.658648e-05 8.751228e-05 8.843033e-05 8.934018e-05
## [71,] 8.493809e-05 8.589420e-05 8.684318e-05 8.778456e-05 8.871790e-05
## [72,] 8.421876e-05 8.519760e-05 8.616949e-05 8.713395e-05 8.809053e-05
## [73,] 8.349573e-05 8.449705e-05 8.549158e-05 8.647886e-05 8.745842e-05
## [74,] 8.276935e-05 8.379288e-05 8.480980e-05 8.581963e-05 8.682189e-05
## [75,] 8.203999e-05 8.308546e-05 8.412450e-05 8.515660e-05 8.618130e-05
## [76,] 8.130798e-05 8.237513e-05 8.343600e-05 8.449012e-05 8.553699e-05
## [77,] 8.057367e-05 8.166221e-05 8.274466e-05 8.382051e-05 8.488927e-05
## [78,] 7.983739e-05 8.094706e-05 8.205080e-05 8.314811e-05 8.423848e-05
## [79,] 7.909946e-05 8.022998e-05 8.135474e-05 8.247323e-05 8.358494e-05
## [80,] 7.836022e-05 7.951130e-05 8.065680e-05 8.179620e-05 8.292897e-05
## [81,] 7.761995e-05 7.879134e-05 7.995730e-05 8.111731e-05 8.227086e-05
## [82,] 7.687899e-05 7.807038e-05 7.925653e-05 8.043689e-05 8.161093e-05
## [83,] 7.613761e-05 7.734875e-05 7.855479e-05 7.975521e-05 8.094947e-05
## [84,] 7.539612e-05 7.662671e-05 7.785237e-05 7.907257e-05 8.028676e-05
## [85,] 7.465478e-05 7.590455e-05 7.714956e-05 7.838926e-05 7.962310e-05
## [86,] 7.391388e-05 7.518255e-05 7.644661e-05 7.770553e-05 7.895874e-05
## [87,] 7.317368e-05 7.446096e-05 7.574381e-05 7.702167e-05 7.829396e-05
## [88,] 7.243442e-05 7.374005e-05 7.504140e-05 7.633792e-05 7.762902e-05
## [89,] 7.169637e-05 7.302006e-05 7.433964e-05 7.565453e-05 7.696416e-05
## [90,] 7.095976e-05 7.230124e-05 7.363877e-05 7.497176e-05 7.629963e-05
## [91,] 7.022481e-05 7.158381e-05 7.293901e-05 7.428982e-05 7.563567e-05
## [92,] 6.949175e-05 7.086799e-05 7.224059e-05 7.360895e-05 7.497249e-05
## [93,] 6.876078e-05 7.015400e-05 7.154372e-05 7.292936e-05 7.431032e-05
## [94,] 6.803212e-05 6.944204e-05 7.084862e-05 7.225127e-05 7.364937e-05
## [95,] 6.730596e-05 6.873232e-05 7.015548e-05 7.157486e-05 7.298984e-05
## [96,] 6.658249e-05 6.802501e-05 6.946450e-05 7.090034e-05 7.233193e-05
## [97,] 6.586187e-05 6.732030e-05 6.877584e-05 7.022789e-05 7.167582e-05
## [98,] 6.514428e-05 6.661836e-05 6.808970e-05 6.955768e-05 7.102169e-05
## [99,] 6.442989e-05 6.591936e-05 6.740623e-05 6.888989e-05 7.036971e-05
## [100,] 6.371885e-05 6.522345e-05 6.672560e-05 6.822467e-05 6.972004e-05
## [,31] [,32] [,33] [,34] [,35]
## [1,] 1.052300e-04 1.043112e-04 1.033767e-04 1.024265e-04 1.014610e-04
## [2,] 1.054081e-04 1.045111e-04 1.035983e-04 1.026699e-04 1.017262e-04
## [3,] 1.055783e-04 1.047033e-04 1.038125e-04 1.029062e-04 1.019846e-04
## [4,] 1.057402e-04 1.048875e-04 1.040190e-04 1.031350e-04 1.022357e-04
## [5,] 1.058936e-04 1.050635e-04 1.042175e-04 1.033561e-04 1.024795e-04
## [6,] 1.060382e-04 1.052309e-04 1.044078e-04 1.035693e-04 1.027155e-04
## [7,] 1.061738e-04 1.053895e-04 1.045895e-04 1.037741e-04 1.029435e-04
## [8,] 1.063000e-04 1.055390e-04 1.047624e-04 1.039704e-04 1.031632e-04
## [9,] 1.064166e-04 1.056792e-04 1.049262e-04 1.041578e-04 1.033743e-04
## [10,] 1.065233e-04 1.058097e-04 1.050806e-04 1.043362e-04 1.035766e-04
## [11,] 1.066199e-04 1.059304e-04 1.052254e-04 1.045051e-04 1.037697e-04
## [12,] 1.067061e-04 1.060409e-04 1.053603e-04 1.046644e-04 1.039534e-04
## [13,] 1.067816e-04 1.061410e-04 1.054850e-04 1.048138e-04 1.041275e-04
## [14,] 1.068462e-04 1.062304e-04 1.055993e-04 1.049529e-04 1.042916e-04
## [15,] 1.068997e-04 1.063089e-04 1.057028e-04 1.050816e-04 1.044454e-04
## [16,] 1.069417e-04 1.063762e-04 1.057955e-04 1.051996e-04 1.045888e-04
## [17,] 1.069722e-04 1.064321e-04 1.058769e-04 1.053066e-04 1.047215e-04
## [18,] 1.069907e-04 1.064764e-04 1.059469e-04 1.054024e-04 1.048431e-04
## [19,] 1.069972e-04 1.065087e-04 1.060052e-04 1.054868e-04 1.049535e-04
## [20,] 1.069914e-04 1.065290e-04 1.060517e-04 1.055595e-04 1.050525e-04
## [21,] 1.069731e-04 1.065370e-04 1.060860e-04 1.056202e-04 1.051397e-04
## [22,] 1.069421e-04 1.065325e-04 1.061081e-04 1.056689e-04 1.052150e-04
## [23,] 1.068982e-04 1.065153e-04 1.061176e-04 1.057052e-04 1.052782e-04
## [24,] 1.068413e-04 1.064852e-04 1.061145e-04 1.057290e-04 1.053290e-04
## [25,] 1.067712e-04 1.064422e-04 1.060985e-04 1.057402e-04 1.053673e-04
## [26,] 1.066878e-04 1.063859e-04 1.060694e-04 1.057384e-04 1.053930e-04
## [27,] 1.065909e-04 1.063163e-04 1.060272e-04 1.057237e-04 1.054057e-04
## [28,] 1.064804e-04 1.062332e-04 1.059717e-04 1.056957e-04 1.054054e-04
## [29,] 1.063563e-04 1.061366e-04 1.059027e-04 1.056545e-04 1.053919e-04
## [30,] 1.062183e-04 1.060263e-04 1.058202e-04 1.055998e-04 1.053651e-04
## [31,] 1.060664e-04 1.059023e-04 1.057240e-04 1.055316e-04 1.053249e-04
## [32,] 1.059007e-04 1.057644e-04 1.056141e-04 1.054497e-04 1.052712e-04
## [33,] 1.057210e-04 1.056127e-04 1.054904e-04 1.053542e-04 1.052039e-04
## [34,] 1.055272e-04 1.054470e-04 1.053529e-04 1.052449e-04 1.051229e-04
## [35,] 1.053195e-04 1.052673e-04 1.052015e-04 1.051218e-04 1.050282e-04
## [36,] 1.050977e-04 1.050738e-04 1.050362e-04 1.049848e-04 1.049196e-04
## [37,] 1.048619e-04 1.048662e-04 1.048569e-04 1.048340e-04 1.047973e-04
## [38,] 1.046122e-04 1.046448e-04 1.046638e-04 1.046693e-04 1.046612e-04
## [39,] 1.043486e-04 1.044094e-04 1.044569e-04 1.044909e-04 1.045113e-04
## [40,] 1.040711e-04 1.041602e-04 1.042361e-04 1.042986e-04 1.043476e-04
## [41,] 1.037799e-04 1.038973e-04 1.040016e-04 1.040925e-04 1.041701e-04
## [42,] 1.034750e-04 1.036207e-04 1.037534e-04 1.038728e-04 1.039790e-04
## [43,] 1.031566e-04 1.033306e-04 1.034916e-04 1.036395e-04 1.037742e-04
## [44,] 1.028248e-04 1.030270e-04 1.032163e-04 1.033927e-04 1.035560e-04
## [45,] 1.024797e-04 1.027101e-04 1.029277e-04 1.031325e-04 1.033243e-04
## [46,] 1.021215e-04 1.023800e-04 1.026260e-04 1.028591e-04 1.030793e-04
## [47,] 1.017504e-04 1.020370e-04 1.023111e-04 1.025726e-04 1.028211e-04
## [48,] 1.013666e-04 1.016812e-04 1.019834e-04 1.022731e-04 1.025500e-04
## [49,] 1.009703e-04 1.013128e-04 1.016430e-04 1.019608e-04 1.022660e-04
## [50,] 1.005617e-04 1.009320e-04 1.012902e-04 1.016360e-04 1.019693e-04
## [51,] 1.001410e-04 1.005390e-04 1.009250e-04 1.012988e-04 1.016601e-04
## [52,] 9.970853e-05 1.001341e-04 1.005478e-04 1.009494e-04 1.013387e-04
## [53,] 9.926450e-05 9.971755e-05 1.001589e-04 1.005881e-04 1.010052e-04
## [54,] 9.880918e-05 9.928955e-05 9.975830e-05 1.002152e-04 1.006599e-04
## [55,] 9.834285e-05 9.885040e-05 9.934646e-05 9.983074e-05 1.003030e-04
## [56,] 9.786581e-05 9.840039e-05 9.892359e-05 9.943514e-05 9.993475e-05
## [57,] 9.737836e-05 9.793979e-05 9.848998e-05 9.902864e-05 9.955546e-05
## [58,] 9.688080e-05 9.746891e-05 9.804592e-05 9.861151e-05 9.916537e-05
## [59,] 9.637344e-05 9.698806e-05 9.759170e-05 9.818404e-05 9.876477e-05
## [60,] 9.585661e-05 9.649754e-05 9.712763e-05 9.774654e-05 9.835394e-05
## [61,] 9.533063e-05 9.599769e-05 9.665402e-05 9.729930e-05 9.793319e-05
## [62,] 9.479585e-05 9.548881e-05 9.617119e-05 9.684263e-05 9.750280e-05
## [63,] 9.425258e-05 9.497125e-05 9.567946e-05 9.637686e-05 9.706310e-05
## [64,] 9.370119e-05 9.444533e-05 9.517916e-05 9.590230e-05 9.661440e-05
## [65,] 9.314200e-05 9.391140e-05 9.467062e-05 9.541928e-05 9.615701e-05
## [66,] 9.257537e-05 9.336980e-05 9.415418e-05 9.492812e-05 9.569125e-05
## [67,] 9.200164e-05 9.282086e-05 9.363017e-05 9.442916e-05 9.521745e-05
## [68,] 9.142117e-05 9.226494e-05 9.309892e-05 9.392272e-05 9.473595e-05
## [69,] 9.083430e-05 9.170237e-05 9.256079e-05 9.340915e-05 9.424705e-05
## [70,] 9.024138e-05 9.113349e-05 9.201610e-05 9.288877e-05 9.375110e-05
## [71,] 8.964275e-05 9.055866e-05 9.146520e-05 9.236193e-05 9.324843e-05
## [72,] 8.903877e-05 8.997822e-05 9.090842e-05 9.182895e-05 9.273936e-05
## [73,] 8.842978e-05 8.939249e-05 9.034610e-05 9.129016e-05 9.222422e-05
## [74,] 8.781612e-05 8.880183e-05 8.977858e-05 9.074590e-05 9.170335e-05
## [75,] 8.719812e-05 8.820656e-05 8.920618e-05 9.019649e-05 9.117705e-05
## [76,] 8.657612e-05 8.760702e-05 8.862923e-05 8.964227e-05 9.064567e-05
## [77,] 8.595044e-05 8.700353e-05 8.804806e-05 8.908354e-05 9.010951e-05
## [78,] 8.532142e-05 8.639642e-05 8.746298e-05 8.852064e-05 8.956889e-05
## [79,] 8.468936e-05 8.578599e-05 8.687432e-05 8.795386e-05 8.902413e-05
## [80,] 8.405459e-05 8.517257e-05 8.628238e-05 8.738353e-05 8.847552e-05
## [81,] 8.341741e-05 8.455646e-05 8.568747e-05 8.680994e-05 8.792338e-05
## [82,] 8.277813e-05 8.393795e-05 8.508988e-05 8.623340e-05 8.736800e-05
## [83,] 8.213703e-05 8.331735e-05 8.448992e-05 8.565419e-05 8.680967e-05
## [84,] 8.149440e-05 8.269494e-05 8.388786e-05 8.507261e-05 8.624868e-05
## [85,] 8.085053e-05 8.207101e-05 8.328399e-05 8.448893e-05 8.568530e-05
## [86,] 8.020569e-05 8.144581e-05 8.267858e-05 8.390343e-05 8.511982e-05
## [87,] 7.956014e-05 8.081963e-05 8.207190e-05 8.331637e-05 8.455251e-05
## [88,] 7.891414e-05 8.019273e-05 8.146420e-05 8.272801e-05 8.398361e-05
## [89,] 7.826796e-05 7.956534e-05 8.085575e-05 8.213862e-05 8.341338e-05
## [90,] 7.762182e-05 7.893773e-05 8.024679e-05 8.154843e-05 8.284208e-05
## [91,] 7.697596e-05 7.831011e-05 7.963755e-05 8.095768e-05 8.226995e-05
## [92,] 7.633062e-05 7.768274e-05 7.902826e-05 8.036661e-05 8.169721e-05
## [93,] 7.568600e-05 7.705582e-05 7.841916e-05 7.977545e-05 8.112409e-05
## [94,] 7.504234e-05 7.642956e-05 7.781045e-05 7.918440e-05 8.055081e-05
## [95,] 7.439982e-05 7.580419e-05 7.720234e-05 7.859367e-05 7.997759e-05
## [96,] 7.375865e-05 7.517989e-05 7.659503e-05 7.800348e-05 7.940462e-05
## [97,] 7.311901e-05 7.455685e-05 7.598873e-05 7.741401e-05 7.883211e-05
## [98,] 7.248109e-05 7.393527e-05 7.538360e-05 7.682546e-05 7.826024e-05
## [99,] 7.184505e-05 7.331531e-05 7.477983e-05 7.623800e-05 7.768920e-05
## [100,] 7.121108e-05 7.269714e-05 7.417759e-05 7.565181e-05 7.711917e-05
## [,36] [,37] [,38] [,39] [,40]
## [1,] 1.004805e-04 9.948528e-05 9.847570e-05 9.745210e-05 9.641486e-05
## [2,] 1.007675e-04 9.979411e-05 9.880631e-05 9.780447e-05 9.678896e-05
## [3,] 1.010479e-04 1.000966e-04 9.913086e-05 9.815107e-05 9.715757e-05
## [4,] 1.013215e-04 1.003925e-04 9.944907e-05 9.849160e-05 9.752039e-05
## [5,] 1.015878e-04 1.006814e-04 9.976066e-05 9.882578e-05 9.787714e-05
## [6,] 1.018467e-04 1.009632e-04 1.000653e-04 9.915333e-05 9.822753e-05
## [7,] 1.020979e-04 1.012376e-04 1.003628e-04 9.947395e-05 9.857126e-05
## [8,] 1.023410e-04 1.015041e-04 1.006528e-04 9.978734e-05 9.890805e-05
## [9,] 1.025758e-04 1.017626e-04 1.009350e-04 1.000932e-04 9.923759e-05
## [10,] 1.028020e-04 1.020128e-04 1.012091e-04 1.003913e-04 9.955958e-05
## [11,] 1.030194e-04 1.022544e-04 1.014749e-04 1.006813e-04 9.987374e-05
## [12,] 1.032276e-04 1.024870e-04 1.017320e-04 1.009629e-04 1.001798e-04
## [13,] 1.034263e-04 1.027105e-04 1.019802e-04 1.012358e-04 1.004774e-04
## [14,] 1.036154e-04 1.029245e-04 1.022192e-04 1.014997e-04 1.007662e-04
## [15,] 1.037944e-04 1.031288e-04 1.024487e-04 1.017544e-04 1.010461e-04
## [16,] 1.039632e-04 1.033230e-04 1.026684e-04 1.019995e-04 1.013167e-04
## [17,] 1.041215e-04 1.035070e-04 1.028780e-04 1.022348e-04 1.015776e-04
## [18,] 1.042690e-04 1.036804e-04 1.030773e-04 1.024601e-04 1.018288e-04
## [19,] 1.044055e-04 1.038430e-04 1.032661e-04 1.026749e-04 1.020697e-04
## [20,] 1.045308e-04 1.039946e-04 1.034440e-04 1.028791e-04 1.023003e-04
## [21,] 1.046445e-04 1.041348e-04 1.036108e-04 1.030725e-04 1.025202e-04
## [22,] 1.047465e-04 1.042636e-04 1.037662e-04 1.032547e-04 1.027291e-04
## [23,] 1.048366e-04 1.043805e-04 1.039101e-04 1.034256e-04 1.029269e-04
## [24,] 1.049145e-04 1.044855e-04 1.040423e-04 1.035848e-04 1.031133e-04
## [25,] 1.049800e-04 1.045783e-04 1.041624e-04 1.037322e-04 1.032880e-04
## [26,] 1.050330e-04 1.046588e-04 1.042703e-04 1.038676e-04 1.034508e-04
## [27,] 1.050733e-04 1.047267e-04 1.043657e-04 1.039907e-04 1.036016e-04
## [28,] 1.051007e-04 1.047818e-04 1.044486e-04 1.041014e-04 1.037400e-04
## [29,] 1.051151e-04 1.048240e-04 1.045188e-04 1.041994e-04 1.038660e-04
## [30,] 1.051163e-04 1.048532e-04 1.045760e-04 1.042847e-04 1.039794e-04
## [31,] 1.051042e-04 1.048692e-04 1.046201e-04 1.043570e-04 1.040799e-04
## [32,] 1.050786e-04 1.048719e-04 1.046511e-04 1.044163e-04 1.041674e-04
## [33,] 1.050396e-04 1.048612e-04 1.046687e-04 1.044623e-04 1.042418e-04
## [34,] 1.049869e-04 1.048370e-04 1.046730e-04 1.044950e-04 1.043030e-04
## [35,] 1.049206e-04 1.047991e-04 1.046637e-04 1.045143e-04 1.043509e-04
## [36,] 1.048406e-04 1.047477e-04 1.046408e-04 1.045200e-04 1.043853e-04
## [37,] 1.047469e-04 1.046825e-04 1.046043e-04 1.045122e-04 1.044062e-04
## [38,] 1.046393e-04 1.046037e-04 1.045541e-04 1.044908e-04 1.044135e-04
## [39,] 1.045180e-04 1.045110e-04 1.044903e-04 1.044557e-04 1.044072e-04
## [40,] 1.043830e-04 1.044047e-04 1.044127e-04 1.044069e-04 1.043873e-04
## [41,] 1.042342e-04 1.042846e-04 1.043214e-04 1.043444e-04 1.043536e-04
## [42,] 1.040717e-04 1.041508e-04 1.042164e-04 1.042682e-04 1.043063e-04
## [43,] 1.038956e-04 1.040034e-04 1.040977e-04 1.041784e-04 1.042453e-04
## [44,] 1.037059e-04 1.038425e-04 1.039655e-04 1.040749e-04 1.041707e-04
## [45,] 1.035028e-04 1.036680e-04 1.038198e-04 1.039579e-04 1.040825e-04
## [46,] 1.032864e-04 1.034802e-04 1.036606e-04 1.038275e-04 1.039808e-04
## [47,] 1.030567e-04 1.032790e-04 1.034881e-04 1.036836e-04 1.038656e-04
## [48,] 1.028139e-04 1.030647e-04 1.033023e-04 1.035265e-04 1.037371e-04
## [49,] 1.025582e-04 1.028375e-04 1.031035e-04 1.033562e-04 1.035953e-04
## [50,] 1.022898e-04 1.025973e-04 1.028917e-04 1.031728e-04 1.034405e-04
## [51,] 1.020087e-04 1.023445e-04 1.026672e-04 1.029766e-04 1.032727e-04
## [52,] 1.017153e-04 1.020792e-04 1.024300e-04 1.027677e-04 1.030920e-04
## [53,] 1.014097e-04 1.018016e-04 1.021805e-04 1.025462e-04 1.028987e-04
## [54,] 1.010922e-04 1.015119e-04 1.019187e-04 1.023124e-04 1.026930e-04
## [55,] 1.007629e-04 1.012103e-04 1.016449e-04 1.020665e-04 1.024749e-04
## [56,] 1.004222e-04 1.008971e-04 1.013593e-04 1.018086e-04 1.022448e-04
## [57,] 1.000702e-04 1.005725e-04 1.010622e-04 1.015391e-04 1.020029e-04
## [58,] 9.970723e-05 1.002368e-04 1.007538e-04 1.012581e-04 1.017493e-04
## [59,] 9.933359e-05 9.989022e-05 1.004344e-04 1.009658e-04 1.014843e-04
## [60,] 9.894955e-05 9.953304e-05 1.001042e-04 1.006626e-04 1.012082e-04
## [61,] 9.855537e-05 9.916555e-05 9.976342e-05 1.003487e-04 1.009212e-04
## [62,] 9.815138e-05 9.878803e-05 9.941246e-05 1.000244e-04 1.006235e-04
## [63,] 9.773785e-05 9.840077e-05 9.905156e-05 9.968991e-05 1.003155e-04
## [64,] 9.731510e-05 9.800408e-05 9.868100e-05 9.934557e-05 9.999747e-05
## [65,] 9.688345e-05 9.759826e-05 9.830110e-05 9.899166e-05 9.966962e-05
## [66,] 9.644320e-05 9.718361e-05 9.791215e-05 9.862847e-05 9.933227e-05
## [67,] 9.599468e-05 9.676046e-05 9.751445e-05 9.825632e-05 9.898572e-05
## [68,] 9.553820e-05 9.632912e-05 9.710833e-05 9.787549e-05 9.863026e-05
## [69,] 9.507409e-05 9.588990e-05 9.669408e-05 9.748630e-05 9.826620e-05
## [70,] 9.460268e-05 9.544312e-05 9.627204e-05 9.708906e-05 9.789383e-05
## [71,] 9.412429e-05 9.498911e-05 9.584250e-05 9.668408e-05 9.751348e-05
## [72,] 9.363925e-05 9.452819e-05 9.540579e-05 9.627166e-05 9.712543e-05
## [73,] 9.314787e-05 9.406067e-05 9.496223e-05 9.585213e-05 9.673001e-05
## [74,] 9.265048e-05 9.358688e-05 9.451212e-05 9.542580e-05 9.632752e-05
## [75,] 9.214742e-05 9.310714e-05 9.405580e-05 9.499297e-05 9.591827e-05
## [76,] 9.163898e-05 9.262176e-05 9.359356e-05 9.455397e-05 9.550257e-05
## [77,] 9.112550e-05 9.213105e-05 9.312572e-05 9.410909e-05 9.508072e-05
## [78,] 9.060728e-05 9.163533e-05 9.265260e-05 9.365864e-05 9.465303e-05
## [79,] 9.008463e-05 9.113490e-05 9.217449e-05 9.320293e-05 9.421979e-05
## [80,] 8.955786e-05 9.063008e-05 9.169169e-05 9.274226e-05 9.378132e-05
## [81,] 8.902728e-05 9.012115e-05 9.120452e-05 9.227692e-05 9.333790e-05
## [82,] 8.849317e-05 8.960841e-05 9.071325e-05 9.180721e-05 9.288982e-05
## [83,] 8.795582e-05 8.909216e-05 9.021819e-05 9.133341e-05 9.243737e-05
## [84,] 8.741554e-05 8.857268e-05 8.971960e-05 9.085582e-05 9.198085e-05
## [85,] 8.687258e-05 8.805025e-05 8.921779e-05 9.037470e-05 9.152051e-05
## [86,] 8.632724e-05 8.752514e-05 8.871301e-05 8.989034e-05 9.105665e-05
## [87,] 8.577977e-05 8.699762e-05 8.820553e-05 8.940300e-05 9.058952e-05
## [88,] 8.523043e-05 8.646795e-05 8.769563e-05 8.891294e-05 9.011939e-05
## [89,] 8.467949e-05 8.593639e-05 8.718355e-05 8.842043e-05 8.964651e-05
## [90,] 8.412719e-05 8.540319e-05 8.666954e-05 8.792570e-05 8.917115e-05
## [91,] 8.357377e-05 8.486859e-05 8.615385e-05 8.742901e-05 8.869353e-05
## [92,] 8.301946e-05 8.433282e-05 8.563671e-05 8.693059e-05 8.821391e-05
## [93,] 8.246450e-05 8.379612e-05 8.511836e-05 8.643068e-05 8.773252e-05
## [94,] 8.190911e-05 8.325870e-05 8.459902e-05 8.592950e-05 8.724958e-05
## [95,] 8.135349e-05 8.272079e-05 8.407890e-05 8.542727e-05 8.676531e-05
## [96,] 8.079785e-05 8.218258e-05 8.355822e-05 8.492419e-05 8.627993e-05
## [97,] 8.024240e-05 8.164429e-05 8.303718e-05 8.442049e-05 8.579364e-05
## [98,] 7.968732e-05 8.110610e-05 8.251597e-05 8.391635e-05 8.530665e-05
## [99,] 7.913281e-05 8.056821e-05 8.199479e-05 8.341197e-05 8.481915e-05
## [100,] 7.857903e-05 8.003079e-05 8.147382e-05 8.290753e-05 8.433132e-05
## [,41] [,42] [,43] [,44] [,45]
## [1,] 9.536436e-05 9.430101e-05 9.322523e-05 9.213745e-05 9.103813e-05
## [2,] 9.576015e-05 9.471845e-05 9.366425e-05 9.259800e-05 9.152012e-05
## [3,] 9.615073e-05 9.513095e-05 9.409862e-05 9.305417e-05 9.199802e-05
## [4,] 9.653581e-05 9.553823e-05 9.452805e-05 9.350569e-05 9.247155e-05
## [5,] 9.691509e-05 9.594000e-05 9.495225e-05 9.395225e-05 9.294041e-05
## [6,] 9.728828e-05 9.633595e-05 9.537092e-05 9.439356e-05 9.340429e-05
## [7,] 9.765510e-05 9.672581e-05 9.578375e-05 9.482932e-05 9.386290e-05
## [8,] 9.801524e-05 9.710925e-05 9.619046e-05 9.525922e-05 9.431593e-05
## [9,] 9.836840e-05 9.748600e-05 9.659073e-05 9.568296e-05 9.476307e-05
## [10,] 9.871428e-05 9.785573e-05 9.698426e-05 9.610023e-05 9.520401e-05
## [11,] 9.905260e-05 9.821815e-05 9.737075e-05 9.651072e-05 9.563843e-05
## [12,] 9.938303e-05 9.857296e-05 9.774988e-05 9.691412e-05 9.606603e-05
## [13,] 9.970530e-05 9.891986e-05 9.812136e-05 9.731012e-05 9.648649e-05
## [14,] 1.000191e-04 9.925853e-05 9.848487e-05 9.769841e-05 9.689949e-05
## [15,] 1.003241e-04 9.958869e-05 9.884011e-05 9.807867e-05 9.730472e-05
## [16,] 1.006201e-04 9.991003e-05 9.918677e-05 9.845061e-05 9.770186e-05
## [17,] 1.009067e-04 1.002223e-04 9.952456e-05 9.881392e-05 9.809061e-05
## [18,] 1.011837e-04 1.005251e-04 9.985318e-05 9.916828e-05 9.847066e-05
## [19,] 1.014508e-04 1.008182e-04 1.001723e-04 9.951341e-05 9.884171e-05
## [20,] 1.017076e-04 1.011014e-04 1.004817e-04 9.984901e-05 9.920344e-05
## [21,] 1.019540e-04 1.013743e-04 1.007811e-04 1.001748e-04 9.955556e-05
## [22,] 1.021897e-04 1.016367e-04 1.010702e-04 1.004905e-04 9.989779e-05
## [23,] 1.024144e-04 1.018883e-04 1.013486e-04 1.007957e-04 1.002298e-04
## [24,] 1.026279e-04 1.021288e-04 1.016162e-04 1.010904e-04 1.005514e-04
## [25,] 1.028299e-04 1.023581e-04 1.018727e-04 1.013741e-04 1.008623e-04
## [26,] 1.030202e-04 1.025758e-04 1.021179e-04 1.016466e-04 1.011621e-04
## [27,] 1.031986e-04 1.027818e-04 1.023515e-04 1.019077e-04 1.014507e-04
## [28,] 1.033648e-04 1.029758e-04 1.025732e-04 1.021571e-04 1.017278e-04
## [29,] 1.035187e-04 1.031576e-04 1.027829e-04 1.023947e-04 1.019931e-04
## [30,] 1.036601e-04 1.033271e-04 1.029804e-04 1.026201e-04 1.022465e-04
## [31,] 1.037888e-04 1.034840e-04 1.031654e-04 1.028333e-04 1.024877e-04
## [32,] 1.039047e-04 1.036281e-04 1.033378e-04 1.030339e-04 1.027166e-04
## [33,] 1.040075e-04 1.037593e-04 1.034974e-04 1.032219e-04 1.029329e-04
## [34,] 1.040972e-04 1.038775e-04 1.036441e-04 1.033970e-04 1.031364e-04
## [35,] 1.041736e-04 1.039825e-04 1.037777e-04 1.035591e-04 1.033270e-04
## [36,] 1.042367e-04 1.040743e-04 1.038981e-04 1.037081e-04 1.035046e-04
## [37,] 1.042864e-04 1.041526e-04 1.040051e-04 1.038439e-04 1.036690e-04
## [38,] 1.043224e-04 1.042175e-04 1.040987e-04 1.039662e-04 1.038201e-04
## [39,] 1.043449e-04 1.042688e-04 1.041789e-04 1.040752e-04 1.039577e-04
## [40,] 1.043538e-04 1.043065e-04 1.042454e-04 1.041705e-04 1.040819e-04
## [41,] 1.043490e-04 1.043306e-04 1.042984e-04 1.042523e-04 1.041925e-04
## [42,] 1.043306e-04 1.043410e-04 1.043377e-04 1.043205e-04 1.042895e-04
## [43,] 1.042984e-04 1.043378e-04 1.043633e-04 1.043749e-04 1.043728e-04
## [44,] 1.042527e-04 1.043208e-04 1.043752e-04 1.044157e-04 1.044424e-04
## [45,] 1.041933e-04 1.042903e-04 1.043735e-04 1.044428e-04 1.044983e-04
## [46,] 1.041203e-04 1.042461e-04 1.043581e-04 1.044562e-04 1.045405e-04
## [47,] 1.040339e-04 1.041884e-04 1.043292e-04 1.044561e-04 1.045690e-04
## [48,] 1.039341e-04 1.041173e-04 1.042867e-04 1.044423e-04 1.045839e-04
## [49,] 1.038209e-04 1.040328e-04 1.042308e-04 1.044150e-04 1.045853e-04
## [50,] 1.036946e-04 1.039350e-04 1.041616e-04 1.043743e-04 1.045731e-04
## [51,] 1.035552e-04 1.038240e-04 1.040790e-04 1.043202e-04 1.045475e-04
## [52,] 1.034028e-04 1.037000e-04 1.039834e-04 1.042530e-04 1.045085e-04
## [53,] 1.032377e-04 1.035631e-04 1.038748e-04 1.041726e-04 1.044564e-04
## [54,] 1.030601e-04 1.034136e-04 1.037533e-04 1.040793e-04 1.043912e-04
## [55,] 1.028700e-04 1.032514e-04 1.036192e-04 1.039731e-04 1.043131e-04
## [56,] 1.026676e-04 1.030770e-04 1.034726e-04 1.038544e-04 1.042222e-04
## [57,] 1.024533e-04 1.028903e-04 1.033136e-04 1.037231e-04 1.041187e-04
## [58,] 1.022272e-04 1.026917e-04 1.031426e-04 1.035796e-04 1.040027e-04
## [59,] 1.019895e-04 1.024814e-04 1.029596e-04 1.034241e-04 1.038746e-04
## [60,] 1.017406e-04 1.022596e-04 1.027650e-04 1.032567e-04 1.037344e-04
## [61,] 1.014805e-04 1.020265e-04 1.025589e-04 1.030776e-04 1.035824e-04
## [62,] 1.012096e-04 1.017824e-04 1.023417e-04 1.028872e-04 1.034188e-04
## [63,] 1.009282e-04 1.015275e-04 1.021134e-04 1.026856e-04 1.032438e-04
## [64,] 1.006364e-04 1.012622e-04 1.018745e-04 1.024731e-04 1.030578e-04
## [65,] 1.003347e-04 1.009866e-04 1.016251e-04 1.022499e-04 1.028609e-04
## [66,] 1.000232e-04 1.007011e-04 1.013656e-04 1.020164e-04 1.026533e-04
## [67,] 9.970236e-05 1.004059e-04 1.010961e-04 1.017727e-04 1.024355e-04
## [68,] 9.937232e-05 1.001014e-04 1.008171e-04 1.015192e-04 1.022075e-04
## [69,] 9.903344e-05 9.978772e-05 1.005287e-04 1.012562e-04 1.019698e-04
## [70,] 9.868602e-05 9.946528e-05 1.002313e-04 1.009838e-04 1.017225e-04
## [71,] 9.833035e-05 9.913435e-05 9.992517e-05 1.007025e-04 1.014660e-04
## [72,] 9.796673e-05 9.879522e-05 9.961057e-05 1.004124e-04 1.012006e-04
## [73,] 9.759548e-05 9.844820e-05 9.928781e-05 1.001140e-04 1.009265e-04
## [74,] 9.721690e-05 9.809358e-05 9.895720e-05 9.980743e-05 1.006440e-04
## [75,] 9.683129e-05 9.773167e-05 9.861903e-05 9.949304e-05 1.003534e-04
## [76,] 9.643896e-05 9.736276e-05 9.827360e-05 9.917113e-05 1.000550e-04
## [77,] 9.604021e-05 9.698717e-05 9.792121e-05 9.884198e-05 9.974912e-05
## [78,] 9.563534e-05 9.660518e-05 9.756215e-05 9.850589e-05 9.943603e-05
## [79,] 9.522465e-05 9.621709e-05 9.719672e-05 9.816315e-05 9.911603e-05
## [80,] 9.480844e-05 9.582321e-05 9.682521e-05 9.781406e-05 9.878939e-05
## [81,] 9.438700e-05 9.542382e-05 9.644792e-05 9.745891e-05 9.845640e-05
## [82,] 9.396063e-05 9.501921e-05 9.606512e-05 9.709797e-05 9.811736e-05
## [83,] 9.352961e-05 9.460966e-05 9.567711e-05 9.673154e-05 9.777255e-05
## [84,] 9.309421e-05 9.419547e-05 9.528417e-05 9.635990e-05 9.742223e-05
## [85,] 9.265473e-05 9.377690e-05 9.488657e-05 9.598331e-05 9.706670e-05
## [86,] 9.221143e-05 9.335423e-05 9.448459e-05 9.560206e-05 9.670622e-05
## [87,] 9.176459e-05 9.292773e-05 9.407849e-05 9.521641e-05 9.634106e-05
## [88,] 9.131445e-05 9.249766e-05 9.366854e-05 9.482663e-05 9.597148e-05
## [89,] 9.086130e-05 9.206429e-05 9.325500e-05 9.443297e-05 9.559775e-05
## [90,] 9.040536e-05 9.162785e-05 9.283812e-05 9.403569e-05 9.522011e-05
## [91,] 8.994690e-05 9.118861e-05 9.241814e-05 9.363504e-05 9.483882e-05
## [92,] 8.948615e-05 9.074679e-05 9.199532e-05 9.323126e-05 9.445413e-05
## [93,] 8.902335e-05 9.030264e-05 9.156989e-05 9.282459e-05 9.406627e-05
## [94,] 8.855872e-05 8.985639e-05 9.114208e-05 9.241526e-05 9.367547e-05
## [95,] 8.809249e-05 8.940827e-05 9.071211e-05 9.200351e-05 9.328197e-05
## [96,] 8.762487e-05 8.895847e-05 9.028020e-05 9.158954e-05 9.288598e-05
## [97,] 8.715607e-05 8.850723e-05 8.984657e-05 9.117357e-05 9.248773e-05
## [98,] 8.668630e-05 8.805474e-05 8.941143e-05 9.075582e-05 9.208742e-05
## [99,] 8.621575e-05 8.760120e-05 8.897496e-05 9.033649e-05 9.168525e-05
## [100,] 8.574460e-05 8.714681e-05 8.853738e-05 8.991577e-05 9.128144e-05
## [,46] [,47] [,48] [,49] [,50]
## [1,] 8.992772e-05 8.880669e-05 8.767554e-05 8.653475e-05 8.538483e-05
## [2,] 9.043107e-05 8.933132e-05 8.822135e-05 8.710163e-05 8.597267e-05
## [3,] 9.093063e-05 8.985244e-05 8.876392e-05 8.766556e-05 8.655784e-05
## [4,] 9.142609e-05 9.036974e-05 8.930297e-05 8.822624e-05 8.714005e-05
## [5,] 9.191716e-05 9.088293e-05 8.983819e-05 8.878338e-05 8.771899e-05
## [6,] 9.240353e-05 9.139171e-05 9.036927e-05 8.933667e-05 8.829436e-05
## [7,] 9.288491e-05 9.189577e-05 9.089592e-05 8.988579e-05 8.886584e-05
## [8,] 9.336099e-05 9.239481e-05 9.141781e-05 9.043044e-05 8.943313e-05
## [9,] 9.383145e-05 9.288850e-05 9.193463e-05 9.097029e-05 8.999590e-05
## [10,] 9.429597e-05 9.337653e-05 9.244607e-05 9.150502e-05 9.055382e-05
## [11,] 9.475426e-05 9.385858e-05 9.295179e-05 9.203432e-05 9.110657e-05
## [12,] 9.520597e-05 9.433433e-05 9.345148e-05 9.255784e-05 9.165381e-05
## [13,] 9.565081e-05 9.480346e-05 9.394482e-05 9.307527e-05 9.219522e-05
## [14,] 9.608845e-05 9.526565e-05 9.443146e-05 9.358626e-05 9.273045e-05
## [15,] 9.651856e-05 9.572057e-05 9.491109e-05 9.409050e-05 9.325918e-05
## [16,] 9.694084e-05 9.616790e-05 9.538338e-05 9.458764e-05 9.378107e-05
## [17,] 9.735497e-05 9.660732e-05 9.584800e-05 9.507736e-05 9.429577e-05
## [18,] 9.776063e-05 9.703851e-05 9.630462e-05 9.555932e-05 9.480296e-05
## [19,] 9.815752e-05 9.746115e-05 9.675294e-05 9.603320e-05 9.530229e-05
## [20,] 9.854531e-05 9.787493e-05 9.719261e-05 9.649867e-05 9.579345e-05
## [21,] 9.892372e-05 9.827954e-05 9.762333e-05 9.695540e-05 9.627609e-05
## [22,] 9.929244e-05 9.867468e-05 9.804479e-05 9.740309e-05 9.674989e-05
## [23,] 9.965118e-05 9.906003e-05 9.845667e-05 9.784141e-05 9.721453e-05
## [24,] 9.999965e-05 9.943531e-05 9.885868e-05 9.827005e-05 9.766969e-05
## [25,] 1.003376e-04 9.980024e-05 9.925052e-05 9.868871e-05 9.811507e-05
## [26,] 1.006647e-04 1.001545e-04 9.963190e-05 9.909709e-05 9.855035e-05
## [27,] 1.009807e-04 1.004979e-04 1.000025e-04 9.949491e-05 9.897525e-05
## [28,] 1.012854e-04 1.008301e-04 1.003622e-04 9.988188e-05 9.938946e-05
## [29,] 1.015785e-04 1.011508e-04 1.007105e-04 1.002577e-04 9.979271e-05
## [30,] 1.018597e-04 1.014599e-04 1.010474e-04 1.006222e-04 1.001847e-04
## [31,] 1.021290e-04 1.017571e-04 1.013724e-04 1.009751e-04 1.005653e-04
## [32,] 1.023859e-04 1.020422e-04 1.016855e-04 1.013160e-04 1.009340e-04
## [33,] 1.026305e-04 1.023149e-04 1.019863e-04 1.016449e-04 1.012908e-04
## [34,] 1.028624e-04 1.025751e-04 1.022747e-04 1.019614e-04 1.016354e-04
## [35,] 1.030814e-04 1.028226e-04 1.025505e-04 1.022655e-04 1.019676e-04
## [36,] 1.032875e-04 1.030571e-04 1.028135e-04 1.025568e-04 1.022871e-04
## [37,] 1.034805e-04 1.032787e-04 1.030635e-04 1.028352e-04 1.025938e-04
## [38,] 1.036603e-04 1.034870e-04 1.033004e-04 1.031005e-04 1.028876e-04
## [39,] 1.038267e-04 1.036821e-04 1.035240e-04 1.033527e-04 1.031682e-04
## [40,] 1.039796e-04 1.038637e-04 1.037343e-04 1.035915e-04 1.034355e-04
## [41,] 1.041190e-04 1.040318e-04 1.039311e-04 1.038169e-04 1.036893e-04
## [42,] 1.042447e-04 1.041863e-04 1.041142e-04 1.040287e-04 1.039297e-04
## [43,] 1.043568e-04 1.043271e-04 1.042838e-04 1.042268e-04 1.041564e-04
## [44,] 1.044552e-04 1.044543e-04 1.044396e-04 1.044113e-04 1.043694e-04
## [45,] 1.045399e-04 1.045677e-04 1.045817e-04 1.045820e-04 1.045686e-04
## [46,] 1.046108e-04 1.046673e-04 1.047100e-04 1.047388e-04 1.047540e-04
## [47,] 1.046681e-04 1.047532e-04 1.048245e-04 1.048819e-04 1.049255e-04
## [48,] 1.047116e-04 1.048254e-04 1.049252e-04 1.050111e-04 1.050831e-04
## [49,] 1.047415e-04 1.048839e-04 1.050122e-04 1.051265e-04 1.052269e-04
## [50,] 1.047579e-04 1.049287e-04 1.050854e-04 1.052281e-04 1.053569e-04
## [51,] 1.047607e-04 1.049599e-04 1.051450e-04 1.053160e-04 1.054730e-04
## [52,] 1.047501e-04 1.049776e-04 1.051910e-04 1.053902e-04 1.055753e-04
## [53,] 1.047262e-04 1.049819e-04 1.052234e-04 1.054507e-04 1.056639e-04
## [54,] 1.046891e-04 1.049729e-04 1.052425e-04 1.054978e-04 1.057389e-04
## [55,] 1.046390e-04 1.049507e-04 1.052482e-04 1.055314e-04 1.058003e-04
## [56,] 1.045759e-04 1.049155e-04 1.052407e-04 1.055517e-04 1.058483e-04
## [57,] 1.045001e-04 1.048673e-04 1.052203e-04 1.055588e-04 1.058830e-04
## [58,] 1.044117e-04 1.048065e-04 1.051869e-04 1.055529e-04 1.059045e-04
## [59,] 1.043109e-04 1.047331e-04 1.051408e-04 1.055342e-04 1.059130e-04
## [60,] 1.041980e-04 1.046473e-04 1.050822e-04 1.055027e-04 1.059086e-04
## [61,] 1.040730e-04 1.045493e-04 1.050113e-04 1.054587e-04 1.058915e-04
## [62,] 1.039362e-04 1.044394e-04 1.049282e-04 1.054024e-04 1.058619e-04
## [63,] 1.037880e-04 1.043178e-04 1.048332e-04 1.053340e-04 1.058200e-04
## [64,] 1.036283e-04 1.041846e-04 1.047264e-04 1.052536e-04 1.057660e-04
## [65,] 1.034577e-04 1.040402e-04 1.046082e-04 1.051616e-04 1.057001e-04
## [66,] 1.032762e-04 1.038847e-04 1.044787e-04 1.050580e-04 1.056226e-04
## [67,] 1.030841e-04 1.037184e-04 1.043382e-04 1.049433e-04 1.055336e-04
## [68,] 1.028817e-04 1.035416e-04 1.041870e-04 1.048176e-04 1.054333e-04
## [69,] 1.026693e-04 1.033545e-04 1.040252e-04 1.046812e-04 1.053222e-04
## [70,] 1.024472e-04 1.031575e-04 1.038532e-04 1.045342e-04 1.052003e-04
## [71,] 1.022155e-04 1.029507e-04 1.036713e-04 1.043771e-04 1.050680e-04
## [72,] 1.019746e-04 1.027344e-04 1.034796e-04 1.042100e-04 1.049255e-04
## [73,] 1.017249e-04 1.025090e-04 1.032785e-04 1.040333e-04 1.047730e-04
## [74,] 1.014665e-04 1.022747e-04 1.030683e-04 1.038472e-04 1.046109e-04
## [75,] 1.011997e-04 1.020318e-04 1.028492e-04 1.036519e-04 1.044395e-04
## [76,] 1.009249e-04 1.017805e-04 1.026216e-04 1.034478e-04 1.042589e-04
## [77,] 1.006423e-04 1.015212e-04 1.023856e-04 1.032351e-04 1.040695e-04
## [78,] 1.003522e-04 1.012542e-04 1.021416e-04 1.030141e-04 1.038716e-04
## [79,] 1.000550e-04 1.009797e-04 1.018899e-04 1.027852e-04 1.036654e-04
## [80,] 9.975082e-05 1.006980e-04 1.016307e-04 1.025485e-04 1.034512e-04
## [81,] 9.944004e-05 1.004095e-04 1.013643e-04 1.023044e-04 1.032292e-04
## [82,] 9.912292e-05 1.001143e-04 1.010911e-04 1.020531e-04 1.029999e-04
## [83,] 9.879974e-05 9.981276e-05 1.008113e-04 1.017949e-04 1.027634e-04
## [84,] 9.847079e-05 9.950519e-05 1.005251e-04 1.015301e-04 1.025200e-04
## [85,] 9.813634e-05 9.919184e-05 1.002328e-04 1.012590e-04 1.022700e-04
## [86,] 9.779666e-05 9.887298e-05 9.993482e-05 1.009818e-04 1.020136e-04
## [87,] 9.745201e-05 9.854888e-05 9.963127e-05 1.006988e-04 1.017512e-04
## [88,] 9.710267e-05 9.821980e-05 9.932247e-05 1.004103e-04 1.014830e-04
## [89,] 9.674890e-05 9.788600e-05 9.900867e-05 1.001165e-04 1.012092e-04
## [90,] 9.639094e-05 9.754775e-05 9.869013e-05 9.981770e-05 1.009301e-04
## [91,] 9.602905e-05 9.720528e-05 9.836711e-05 9.951413e-05 1.006460e-04
## [92,] 9.566347e-05 9.685885e-05 9.803984e-05 9.920604e-05 1.003571e-04
## [93,] 9.529445e-05 9.650870e-05 9.770858e-05 9.889368e-05 1.000636e-04
## [94,] 9.492222e-05 9.615506e-05 9.737356e-05 9.857729e-05 9.976585e-05
## [95,] 9.454701e-05 9.579817e-05 9.703501e-05 9.825709e-05 9.946402e-05
## [96,] 9.416904e-05 9.543825e-05 9.669316e-05 9.793333e-05 9.915835e-05
## [97,] 9.378853e-05 9.507552e-05 9.634823e-05 9.760622e-05 9.884906e-05
## [98,] 9.340570e-05 9.471020e-05 9.600044e-05 9.727598e-05 9.853638e-05
## [99,] 9.302075e-05 9.434249e-05 9.565000e-05 9.694282e-05 9.822052e-05
## [100,] 9.263388e-05 9.397260e-05 9.529711e-05 9.660696e-05 9.790169e-05
## [,51] [,52] [,53] [,54] [,55]
## [1,] 8.422630e-05 8.305966e-05 8.188545e-05 8.070418e-05 7.951640e-05
## [2,] 8.483497e-05 8.368904e-05 8.253539e-05 8.137456e-05 8.020705e-05
## [3,] 8.544126e-05 8.431631e-05 8.318352e-05 8.204339e-05 8.089644e-05
## [4,] 8.604486e-05 8.494119e-05 8.382953e-05 8.271039e-05 8.158428e-05
## [5,] 8.664549e-05 8.556337e-05 8.447312e-05 8.337525e-05 8.227026e-05
## [6,] 8.724282e-05 8.618253e-05 8.511398e-05 8.403766e-05 8.295406e-05
## [7,] 8.783655e-05 8.679837e-05 8.575179e-05 8.469729e-05 8.363537e-05
## [8,] 8.842635e-05 8.741056e-05 8.638623e-05 8.535383e-05 8.431385e-05
## [9,] 8.901191e-05 8.801878e-05 8.701697e-05 8.600695e-05 8.498919e-05
## [10,] 8.959289e-05 8.862269e-05 8.764368e-05 8.665630e-05 8.566104e-05
## [11,] 9.016897e-05 8.922198e-05 8.826602e-05 8.730156e-05 8.632906e-05
## [12,] 9.073981e-05 8.981628e-05 8.888366e-05 8.794238e-05 8.699290e-05
## [13,] 9.130508e-05 9.040528e-05 8.949624e-05 8.857840e-05 8.765221e-05
## [14,] 9.186443e-05 9.098862e-05 9.010343e-05 8.920929e-05 8.830664e-05
## [15,] 9.241753e-05 9.156596e-05 9.070487e-05 8.983469e-05 8.895584e-05
## [16,] 9.296404e-05 9.213695e-05 9.130022e-05 9.045424e-05 8.959943e-05
## [17,] 9.350361e-05 9.270126e-05 9.188911e-05 9.106758e-05 9.023707e-05
## [18,] 9.403590e-05 9.325852e-05 9.247121e-05 9.167437e-05 9.086840e-05
## [19,] 9.456057e-05 9.380840e-05 9.304617e-05 9.227425e-05 9.149304e-05
## [20,] 9.507729e-05 9.435056e-05 9.361362e-05 9.286685e-05 9.211064e-05
## [21,] 9.558571e-05 9.488464e-05 9.417322e-05 9.345183e-05 9.272083e-05
## [22,] 9.608552e-05 9.541031e-05 9.472463e-05 9.402883e-05 9.332327e-05
## [23,] 9.657636e-05 9.592724e-05 9.526750e-05 9.459750e-05 9.391759e-05
## [24,] 9.705794e-05 9.643510e-05 9.580150e-05 9.515750e-05 9.450343e-05
## [25,] 9.752991e-05 9.693355e-05 9.632629e-05 9.570848e-05 9.508046e-05
## [26,] 9.799198e-05 9.742227e-05 9.684155e-05 9.625012e-05 9.564832e-05
## [27,] 9.844383e-05 9.790096e-05 9.734694e-05 9.678207e-05 9.620669e-05
## [28,] 9.888518e-05 9.836931e-05 9.784216e-05 9.730402e-05 9.675522e-05
## [29,] 9.931571e-05 9.882702e-05 9.832690e-05 9.781565e-05 9.729359e-05
## [30,] 9.973517e-05 9.927379e-05 9.880085e-05 9.831666e-05 9.782148e-05
## [31,] 1.001433e-04 9.970935e-05 9.926374e-05 9.880673e-05 9.833860e-05
## [32,] 1.005398e-04 1.001334e-04 9.971528e-05 9.928559e-05 9.884463e-05
## [33,] 1.009244e-04 1.005458e-04 1.001552e-04 9.975296e-05 9.933930e-05
## [34,] 1.012969e-04 1.009461e-04 1.005832e-04 1.002086e-04 9.982232e-05
## [35,] 1.016571e-04 1.013342e-04 1.009992e-04 1.006521e-04 1.002934e-04
## [36,] 1.020048e-04 1.017099e-04 1.014027e-04 1.010835e-04 1.007524e-04
## [37,] 1.023397e-04 1.020729e-04 1.017937e-04 1.015023e-04 1.011989e-04
## [38,] 1.026617e-04 1.024231e-04 1.021719e-04 1.019084e-04 1.016328e-04
## [39,] 1.029706e-04 1.027602e-04 1.025372e-04 1.023017e-04 1.020539e-04
## [40,] 1.032663e-04 1.030842e-04 1.028893e-04 1.026818e-04 1.024619e-04
## [41,] 1.035486e-04 1.033948e-04 1.032281e-04 1.030486e-04 1.028567e-04
## [42,] 1.038174e-04 1.036919e-04 1.035534e-04 1.034021e-04 1.032380e-04
## [43,] 1.040725e-04 1.039754e-04 1.038651e-04 1.037419e-04 1.036059e-04
## [44,] 1.043140e-04 1.042452e-04 1.041632e-04 1.040681e-04 1.039600e-04
## [45,] 1.045416e-04 1.045012e-04 1.044474e-04 1.043804e-04 1.043004e-04
## [46,] 1.047554e-04 1.047433e-04 1.047178e-04 1.046789e-04 1.046268e-04
## [47,] 1.049553e-04 1.049715e-04 1.049742e-04 1.049634e-04 1.049393e-04
## [48,] 1.051414e-04 1.051858e-04 1.052166e-04 1.052338e-04 1.052376e-04
## [49,] 1.053134e-04 1.053861e-04 1.054450e-04 1.054902e-04 1.055219e-04
## [50,] 1.054716e-04 1.055724e-04 1.056593e-04 1.057325e-04 1.057920e-04
## [51,] 1.056158e-04 1.057447e-04 1.058596e-04 1.059606e-04 1.060479e-04
## [52,] 1.057462e-04 1.059031e-04 1.060459e-04 1.061747e-04 1.062896e-04
## [53,] 1.058628e-04 1.060476e-04 1.062182e-04 1.063747e-04 1.065171e-04
## [54,] 1.059656e-04 1.061782e-04 1.063765e-04 1.065606e-04 1.067305e-04
## [55,] 1.060548e-04 1.062950e-04 1.065209e-04 1.067325e-04 1.069298e-04
## [56,] 1.061305e-04 1.063982e-04 1.066516e-04 1.068905e-04 1.071151e-04
## [57,] 1.061926e-04 1.064878e-04 1.067685e-04 1.070347e-04 1.072864e-04
## [58,] 1.062415e-04 1.065639e-04 1.068718e-04 1.071651e-04 1.074438e-04
## [59,] 1.062772e-04 1.066267e-04 1.069616e-04 1.072819e-04 1.075874e-04
## [60,] 1.062998e-04 1.066764e-04 1.070381e-04 1.073852e-04 1.077174e-04
## [61,] 1.063096e-04 1.067129e-04 1.071014e-04 1.074751e-04 1.078339e-04
## [62,] 1.063067e-04 1.067367e-04 1.071517e-04 1.075518e-04 1.079370e-04
## [63,] 1.062913e-04 1.067477e-04 1.071891e-04 1.076155e-04 1.080269e-04
## [64,] 1.062636e-04 1.067462e-04 1.072138e-04 1.076663e-04 1.081037e-04
## [65,] 1.062238e-04 1.067325e-04 1.072260e-04 1.077044e-04 1.081676e-04
## [66,] 1.061721e-04 1.067066e-04 1.072260e-04 1.077301e-04 1.082188e-04
## [67,] 1.061088e-04 1.066689e-04 1.072138e-04 1.077434e-04 1.082576e-04
## [68,] 1.060341e-04 1.066196e-04 1.071898e-04 1.077447e-04 1.082840e-04
## [69,] 1.059481e-04 1.065588e-04 1.071542e-04 1.077341e-04 1.082984e-04
## [70,] 1.058512e-04 1.064869e-04 1.071072e-04 1.077119e-04 1.083010e-04
## [71,] 1.057437e-04 1.064041e-04 1.070490e-04 1.076783e-04 1.082919e-04
## [72,] 1.056257e-04 1.063106e-04 1.069799e-04 1.076336e-04 1.082715e-04
## [73,] 1.054975e-04 1.062066e-04 1.069002e-04 1.075780e-04 1.082400e-04
## [74,] 1.053595e-04 1.060926e-04 1.068100e-04 1.075117e-04 1.081975e-04
## [75,] 1.052118e-04 1.059686e-04 1.067098e-04 1.074351e-04 1.081444e-04
## [76,] 1.050547e-04 1.058350e-04 1.065996e-04 1.073483e-04 1.080810e-04
## [77,] 1.048886e-04 1.056921e-04 1.064799e-04 1.072517e-04 1.080075e-04
## [78,] 1.047137e-04 1.055401e-04 1.063508e-04 1.071455e-04 1.079241e-04
## [79,] 1.045302e-04 1.053794e-04 1.062127e-04 1.070300e-04 1.078311e-04
## [80,] 1.043384e-04 1.052100e-04 1.060658e-04 1.069054e-04 1.077288e-04
## [81,] 1.041387e-04 1.050325e-04 1.059103e-04 1.067721e-04 1.076175e-04
## [82,] 1.039313e-04 1.048469e-04 1.057467e-04 1.066302e-04 1.074974e-04
## [83,] 1.037164e-04 1.046537e-04 1.055750e-04 1.064801e-04 1.073688e-04
## [84,] 1.034944e-04 1.044530e-04 1.053956e-04 1.063220e-04 1.072319e-04
## [85,] 1.032655e-04 1.042452e-04 1.052089e-04 1.061563e-04 1.070871e-04
## [86,] 1.030299e-04 1.040305e-04 1.050149e-04 1.059830e-04 1.069346e-04
## [87,] 1.027881e-04 1.038091e-04 1.048141e-04 1.058027e-04 1.067747e-04
## [88,] 1.025401e-04 1.035814e-04 1.046066e-04 1.056154e-04 1.066076e-04
## [89,] 1.022863e-04 1.033476e-04 1.043928e-04 1.054215e-04 1.064335e-04
## [90,] 1.020270e-04 1.031080e-04 1.041728e-04 1.052212e-04 1.062529e-04
## [91,] 1.017623e-04 1.028627e-04 1.039470e-04 1.050148e-04 1.060658e-04
## [92,] 1.014926e-04 1.026122e-04 1.037156e-04 1.048025e-04 1.058726e-04
## [93,] 1.012180e-04 1.023565e-04 1.034788e-04 1.045845e-04 1.056734e-04
## [94,] 1.009389e-04 1.020960e-04 1.032369e-04 1.043612e-04 1.054687e-04
## [95,] 1.006554e-04 1.018309e-04 1.029901e-04 1.041328e-04 1.052585e-04
## [96,] 1.003678e-04 1.015614e-04 1.027387e-04 1.038994e-04 1.050432e-04
## [97,] 1.000764e-04 1.012878e-04 1.024829e-04 1.036614e-04 1.048229e-04
## [98,] 9.978125e-05 1.010102e-04 1.022229e-04 1.034189e-04 1.045979e-04
## [99,] 9.948269e-05 1.007289e-04 1.019589e-04 1.031722e-04 1.043685e-04
## [100,] 9.918090e-05 1.004442e-04 1.016911e-04 1.029214e-04 1.041347e-04
## [,56] [,57] [,58] [,59] [,60]
## [1,] 7.832264e-05 7.712343e-05 7.591930e-05 7.471080e-05 7.349845e-05
## [2,] 7.903341e-05 7.785415e-05 7.666981e-05 7.548092e-05 7.428801e-05
## [3,] 7.974320e-05 7.858418e-05 7.741991e-05 7.625090e-05 7.507770e-05
## [4,] 8.045171e-05 7.931321e-05 7.816928e-05 7.702045e-05 7.586722e-05
## [5,] 8.115865e-05 8.004094e-05 7.891763e-05 7.778924e-05 7.665627e-05
## [6,] 8.186369e-05 8.076704e-05 7.966463e-05 7.855696e-05 7.744453e-05
## [7,] 8.256651e-05 8.149121e-05 8.040997e-05 7.932329e-05 7.823166e-05
## [8,] 8.326678e-05 8.221310e-05 8.115331e-05 8.008789e-05 7.901734e-05
## [9,] 8.396418e-05 8.293239e-05 8.189431e-05 8.085043e-05 7.980122e-05
## [10,] 8.465835e-05 8.364873e-05 8.263263e-05 8.161055e-05 8.058296e-05
## [11,] 8.534897e-05 8.436177e-05 8.336793e-05 8.236791e-05 8.136220e-05
## [12,] 8.603567e-05 8.507116e-05 8.409984e-05 8.312216e-05 8.213859e-05
## [13,] 8.671811e-05 8.577655e-05 8.482800e-05 8.387291e-05 8.291174e-05
## [14,] 8.739592e-05 8.647758e-05 8.555206e-05 8.461982e-05 8.368130e-05
## [15,] 8.806875e-05 8.717387e-05 8.627164e-05 8.536249e-05 8.444689e-05
## [16,] 8.873623e-05 8.786507e-05 8.698637e-05 8.610057e-05 8.520812e-05
## [17,] 8.939800e-05 8.855080e-05 8.769587e-05 8.683367e-05 8.596462e-05
## [18,] 9.005370e-05 8.923068e-05 8.839978e-05 8.756141e-05 8.671600e-05
## [19,] 9.070294e-05 8.990436e-05 8.909771e-05 8.828341e-05 8.746187e-05
## [20,] 9.134537e-05 9.057145e-05 8.978929e-05 8.899928e-05 8.820183e-05
## [21,] 9.198062e-05 9.123159e-05 9.047413e-05 8.970863e-05 8.893551e-05
## [22,] 9.260833e-05 9.188440e-05 9.115185e-05 9.041109e-05 8.966252e-05
## [23,] 9.322813e-05 9.252951e-05 9.182209e-05 9.110628e-05 9.038245e-05
## [24,] 9.383966e-05 9.316655e-05 9.248447e-05 9.179381e-05 9.109493e-05
## [25,] 9.444257e-05 9.379517e-05 9.313862e-05 9.247330e-05 9.179957e-05
## [26,] 9.503650e-05 9.441500e-05 9.378417e-05 9.314438e-05 9.249599e-05
## [27,] 9.562111e-05 9.502569e-05 9.442076e-05 9.380668e-05 9.318381e-05
## [28,] 9.619606e-05 9.562688e-05 9.504803e-05 9.445984e-05 9.386267e-05
## [29,] 9.676101e-05 9.621825e-05 9.566563e-05 9.510350e-05 9.453218e-05
## [30,] 9.731565e-05 9.679945e-05 9.627323e-05 9.573730e-05 9.519200e-05
## [31,] 9.785964e-05 9.737017e-05 9.687048e-05 9.636090e-05 9.584177e-05
## [32,] 9.839269e-05 9.793007e-05 9.745706e-05 9.697398e-05 9.648114e-05
## [33,] 9.891450e-05 9.847886e-05 9.803265e-05 9.757619e-05 9.710979e-05
## [34,] 9.942478e-05 9.901623e-05 9.859695e-05 9.816723e-05 9.772738e-05
## [35,] 9.992326e-05 9.954191e-05 9.914966e-05 9.874679e-05 9.833360e-05
## [36,] 1.004097e-04 1.000556e-04 9.969049e-05 9.931458e-05 9.892815e-05
## [37,] 1.008837e-04 1.005571e-04 1.002192e-04 9.987031e-05 9.951074e-05
## [38,] 1.013453e-04 1.010461e-04 1.007355e-04 1.004137e-04 1.000811e-04
## [39,] 1.017940e-04 1.015224e-04 1.012391e-04 1.009445e-04 1.006389e-04
## [40,] 1.022298e-04 1.019857e-04 1.017299e-04 1.014626e-04 1.011840e-04
## [41,] 1.026523e-04 1.024359e-04 1.022075e-04 1.019675e-04 1.017161e-04
## [42,] 1.030615e-04 1.028728e-04 1.026719e-04 1.024592e-04 1.022349e-04
## [43,] 1.034572e-04 1.032961e-04 1.031228e-04 1.029375e-04 1.027403e-04
## [44,] 1.038392e-04 1.037058e-04 1.035600e-04 1.034021e-04 1.032321e-04
## [45,] 1.042074e-04 1.041017e-04 1.039835e-04 1.038529e-04 1.037102e-04
## [46,] 1.045617e-04 1.044837e-04 1.043930e-04 1.042898e-04 1.041742e-04
## [47,] 1.049019e-04 1.048516e-04 1.047884e-04 1.047126e-04 1.046242e-04
## [48,] 1.052281e-04 1.052054e-04 1.051697e-04 1.051212e-04 1.050600e-04
## [49,] 1.055401e-04 1.055450e-04 1.055367e-04 1.055155e-04 1.054814e-04
## [50,] 1.058378e-04 1.058703e-04 1.058894e-04 1.058954e-04 1.058884e-04
## [51,] 1.061214e-04 1.061813e-04 1.062278e-04 1.062610e-04 1.062810e-04
## [52,] 1.063906e-04 1.064780e-04 1.065517e-04 1.066120e-04 1.066590e-04
## [53,] 1.066456e-04 1.067603e-04 1.068612e-04 1.069485e-04 1.070224e-04
## [54,] 1.068864e-04 1.070283e-04 1.071563e-04 1.072706e-04 1.073712e-04
## [55,] 1.071130e-04 1.072820e-04 1.074370e-04 1.075781e-04 1.077054e-04
## [56,] 1.073254e-04 1.075214e-04 1.077033e-04 1.078711e-04 1.080250e-04
## [57,] 1.075237e-04 1.077466e-04 1.079553e-04 1.081497e-04 1.083301e-04
## [58,] 1.077080e-04 1.079577e-04 1.081930e-04 1.084139e-04 1.086206e-04
## [59,] 1.078784e-04 1.081547e-04 1.084165e-04 1.086638e-04 1.088967e-04
## [60,] 1.080349e-04 1.083377e-04 1.086259e-04 1.088994e-04 1.091584e-04
## [61,] 1.081778e-04 1.085070e-04 1.088213e-04 1.091208e-04 1.094057e-04
## [62,] 1.083072e-04 1.086625e-04 1.090028e-04 1.093283e-04 1.096389e-04
## [63,] 1.084231e-04 1.088044e-04 1.091706e-04 1.095218e-04 1.098580e-04
## [64,] 1.085259e-04 1.089329e-04 1.093248e-04 1.097015e-04 1.100632e-04
## [65,] 1.086155e-04 1.090481e-04 1.094655e-04 1.098676e-04 1.102545e-04
## [66,] 1.086923e-04 1.091503e-04 1.095930e-04 1.100203e-04 1.104322e-04
## [67,] 1.087563e-04 1.092396e-04 1.097074e-04 1.101596e-04 1.105965e-04
## [68,] 1.088079e-04 1.093162e-04 1.098088e-04 1.102859e-04 1.107474e-04
## [69,] 1.088472e-04 1.093802e-04 1.098976e-04 1.103992e-04 1.108852e-04
## [70,] 1.088744e-04 1.094320e-04 1.099739e-04 1.104999e-04 1.110101e-04
## [71,] 1.088898e-04 1.094718e-04 1.100379e-04 1.105880e-04 1.111222e-04
## [72,] 1.088936e-04 1.094997e-04 1.100898e-04 1.106639e-04 1.112219e-04
## [73,] 1.088860e-04 1.095160e-04 1.101299e-04 1.107276e-04 1.113092e-04
## [74,] 1.088673e-04 1.095209e-04 1.101584e-04 1.107796e-04 1.113845e-04
## [75,] 1.088377e-04 1.095148e-04 1.101755e-04 1.108200e-04 1.114480e-04
## [76,] 1.087975e-04 1.094977e-04 1.101816e-04 1.108490e-04 1.114999e-04
## [77,] 1.087470e-04 1.094701e-04 1.101768e-04 1.108669e-04 1.115405e-04
## [78,] 1.086863e-04 1.094321e-04 1.101614e-04 1.108740e-04 1.115700e-04
## [79,] 1.086158e-04 1.093841e-04 1.101356e-04 1.108705e-04 1.115886e-04
## [80,] 1.085358e-04 1.093262e-04 1.100998e-04 1.108567e-04 1.115967e-04
## [81,] 1.084464e-04 1.092587e-04 1.100542e-04 1.108328e-04 1.115944e-04
## [82,] 1.083480e-04 1.091819e-04 1.099990e-04 1.107991e-04 1.115821e-04
## [83,] 1.082409e-04 1.090961e-04 1.099345e-04 1.107558e-04 1.115600e-04
## [84,] 1.081252e-04 1.090016e-04 1.098610e-04 1.107033e-04 1.115283e-04
## [85,] 1.080013e-04 1.088985e-04 1.097787e-04 1.106417e-04 1.114874e-04
## [86,] 1.078694e-04 1.087873e-04 1.096880e-04 1.105714e-04 1.114374e-04
## [87,] 1.077299e-04 1.086680e-04 1.095890e-04 1.104926e-04 1.113787e-04
## [88,] 1.075828e-04 1.085411e-04 1.094820e-04 1.104055e-04 1.113115e-04
## [89,] 1.074287e-04 1.084067e-04 1.093674e-04 1.103105e-04 1.112361e-04
## [90,] 1.072676e-04 1.082651e-04 1.092452e-04 1.102078e-04 1.111527e-04
## [91,] 1.070998e-04 1.081166e-04 1.091159e-04 1.100977e-04 1.110616e-04
## [92,] 1.069256e-04 1.079614e-04 1.089797e-04 1.099803e-04 1.109631e-04
## [93,] 1.067453e-04 1.077998e-04 1.088368e-04 1.098560e-04 1.108573e-04
## [94,] 1.065591e-04 1.076320e-04 1.086874e-04 1.097250e-04 1.107447e-04
## [95,] 1.063671e-04 1.074583e-04 1.085319e-04 1.095876e-04 1.106253e-04
## [96,] 1.061698e-04 1.072789e-04 1.083704e-04 1.094440e-04 1.104994e-04
## [97,] 1.059673e-04 1.070941e-04 1.082032e-04 1.092943e-04 1.103673e-04
## [98,] 1.057597e-04 1.069040e-04 1.080305e-04 1.091390e-04 1.102293e-04
## [99,] 1.055475e-04 1.067090e-04 1.078526e-04 1.089782e-04 1.100854e-04
## [100,] 1.053307e-04 1.065091e-04 1.076696e-04 1.088120e-04 1.099361e-04
## [,61] [,62] [,63] [,64] [,65]
## [1,] 7.228279e-05 7.106433e-05 6.984361e-05 6.862113e-05 6.739741e-05
## [2,] 7.309159e-05 7.189219e-05 7.069032e-05 6.948651e-05 6.828124e-05
## [3,] 7.390080e-05 7.272073e-05 7.153800e-05 7.035311e-05 6.916657e-05
## [4,] 7.471012e-05 7.354965e-05 7.238633e-05 7.122064e-05 7.005310e-05
## [5,] 7.551924e-05 7.437865e-05 7.323500e-05 7.208878e-05 7.094050e-05
## [6,] 7.632784e-05 7.520739e-05 7.408369e-05 7.295722e-05 7.182846e-05
## [7,] 7.713558e-05 7.603556e-05 7.493207e-05 7.382560e-05 7.271665e-05
## [8,] 7.794215e-05 7.686281e-05 7.577980e-05 7.469361e-05 7.360472e-05
## [9,] 7.874719e-05 7.768880e-05 7.662654e-05 7.556089e-05 7.449232e-05
## [10,] 7.955034e-05 7.851318e-05 7.747193e-05 7.642708e-05 7.537910e-05
## [11,] 8.035127e-05 7.933558e-05 7.831561e-05 7.729183e-05 7.626470e-05
## [12,] 8.114960e-05 8.015565e-05 7.915722e-05 7.815475e-05 7.714872e-05
## [13,] 8.194496e-05 8.097301e-05 7.999637e-05 7.901548e-05 7.803081e-05
## [14,] 8.273697e-05 8.178728e-05 8.083268e-05 7.987362e-05 7.891056e-05
## [15,] 8.352527e-05 8.259808e-05 8.166577e-05 8.072880e-05 7.978759e-05
## [16,] 8.430946e-05 8.340502e-05 8.249526e-05 8.158060e-05 8.066149e-05
## [17,] 8.508916e-05 8.420771e-05 8.332073e-05 8.242863e-05 8.153187e-05
## [18,] 8.586397e-05 8.500576e-05 8.414179e-05 8.327250e-05 8.239830e-05
## [19,] 8.663351e-05 8.579876e-05 8.495804e-05 8.411178e-05 8.326040e-05
## [20,] 8.739738e-05 8.658632e-05 8.576908e-05 8.494608e-05 8.411772e-05
## [21,] 8.815518e-05 8.736804e-05 8.657450e-05 8.577497e-05 8.496987e-05
## [22,] 8.890652e-05 8.814351e-05 8.737388e-05 8.659805e-05 8.581641e-05
## [23,] 8.965100e-05 8.891233e-05 8.816683e-05 8.741490e-05 8.665694e-05
## [24,] 9.038823e-05 8.967410e-05 8.895293e-05 8.822511e-05 8.749103e-05
## [25,] 9.111782e-05 9.042843e-05 8.973178e-05 8.902826e-05 8.831826e-05
## [26,] 9.183938e-05 9.117492e-05 9.050298e-05 8.982395e-05 8.913821e-05
## [27,] 9.255252e-05 9.191317e-05 9.126613e-05 9.061177e-05 8.995048e-05
## [28,] 9.325686e-05 9.264280e-05 9.202082e-05 9.139132e-05 9.075464e-05
## [29,] 9.395204e-05 9.336342e-05 9.276668e-05 9.216219e-05 9.155030e-05
## [30,] 9.463767e-05 9.407466e-05 9.350332e-05 9.292399e-05 9.233705e-05
## [31,] 9.531340e-05 9.477615e-05 9.423035e-05 9.367635e-05 9.311450e-05
## [32,] 9.597888e-05 9.546752e-05 9.494741e-05 9.441887e-05 9.388225e-05
## [33,] 9.663376e-05 9.614843e-05 9.565413e-05 9.515118e-05 9.463994e-05
## [34,] 9.727771e-05 9.681853e-05 9.635016e-05 9.587293e-05 9.538718e-05
## [35,] 9.791039e-05 9.747748e-05 9.703516e-05 9.658376e-05 9.612362e-05
## [36,] 9.853151e-05 9.812496e-05 9.770879e-05 9.728333e-05 9.684890e-05
## [37,] 9.914075e-05 9.876066e-05 9.837074e-05 9.797131e-05 9.756268e-05
## [38,] 9.973784e-05 9.938428e-05 9.902069e-05 9.864737e-05 9.826463e-05
## [39,] 1.003225e-04 9.999553e-05 9.965835e-05 9.931122e-05 9.895445e-05
## [40,] 1.008944e-04 1.005941e-04 1.002834e-04 9.996256e-05 9.963181e-05
## [41,] 1.014534e-04 1.011799e-04 1.008957e-04 1.006011e-04 1.002964e-04
## [42,] 1.019992e-04 1.017525e-04 1.014948e-04 1.012266e-04 1.009481e-04
## [43,] 1.025317e-04 1.023117e-04 1.020806e-04 1.018388e-04 1.015864e-04
## [44,] 1.030505e-04 1.028573e-04 1.026529e-04 1.024375e-04 1.022113e-04
## [45,] 1.035555e-04 1.033892e-04 1.032114e-04 1.030224e-04 1.028224e-04
## [46,] 1.040466e-04 1.039071e-04 1.037559e-04 1.035933e-04 1.034196e-04
## [47,] 1.045236e-04 1.044109e-04 1.042863e-04 1.041501e-04 1.040026e-04
## [48,] 1.049863e-04 1.049004e-04 1.048024e-04 1.046927e-04 1.045713e-04
## [49,] 1.054347e-04 1.053755e-04 1.053042e-04 1.052207e-04 1.051256e-04
## [50,] 1.058686e-04 1.058362e-04 1.057913e-04 1.057342e-04 1.056652e-04
## [51,] 1.062880e-04 1.062822e-04 1.062638e-04 1.062330e-04 1.061901e-04
## [52,] 1.066928e-04 1.067136e-04 1.067216e-04 1.067171e-04 1.067001e-04
## [53,] 1.070829e-04 1.071303e-04 1.071646e-04 1.071862e-04 1.071952e-04
## [54,] 1.074583e-04 1.075321e-04 1.075928e-04 1.076404e-04 1.076753e-04
## [55,] 1.078191e-04 1.079192e-04 1.080060e-04 1.080797e-04 1.081403e-04
## [56,] 1.081651e-04 1.082915e-04 1.084044e-04 1.085039e-04 1.085903e-04
## [57,] 1.084965e-04 1.086490e-04 1.087879e-04 1.089132e-04 1.090251e-04
## [58,] 1.088132e-04 1.089918e-04 1.091564e-04 1.093074e-04 1.094448e-04
## [59,] 1.091153e-04 1.093198e-04 1.095102e-04 1.096867e-04 1.098495e-04
## [60,] 1.094029e-04 1.096331e-04 1.098491e-04 1.100510e-04 1.102391e-04
## [61,] 1.096760e-04 1.099319e-04 1.101733e-04 1.104005e-04 1.106136e-04
## [62,] 1.099348e-04 1.102161e-04 1.104829e-04 1.107352e-04 1.109732e-04
## [63,] 1.101794e-04 1.104860e-04 1.107778e-04 1.110551e-04 1.113180e-04
## [64,] 1.104098e-04 1.107415e-04 1.110584e-04 1.113605e-04 1.116479e-04
## [65,] 1.106263e-04 1.109829e-04 1.113246e-04 1.116513e-04 1.119632e-04
## [66,] 1.108289e-04 1.112103e-04 1.115766e-04 1.119278e-04 1.122640e-04
## [67,] 1.110179e-04 1.114239e-04 1.118145e-04 1.121900e-04 1.125503e-04
## [68,] 1.111933e-04 1.116237e-04 1.120386e-04 1.124382e-04 1.128224e-04
## [69,] 1.113554e-04 1.118100e-04 1.122490e-04 1.126724e-04 1.130804e-04
## [70,] 1.115044e-04 1.119830e-04 1.124458e-04 1.128929e-04 1.133244e-04
## [71,] 1.116405e-04 1.121428e-04 1.126292e-04 1.130998e-04 1.135547e-04
## [72,] 1.117638e-04 1.122897e-04 1.127995e-04 1.132934e-04 1.137713e-04
## [73,] 1.118746e-04 1.124238e-04 1.129569e-04 1.134738e-04 1.139747e-04
## [74,] 1.119732e-04 1.125455e-04 1.131015e-04 1.136413e-04 1.141648e-04
## [75,] 1.120596e-04 1.126548e-04 1.132336e-04 1.137960e-04 1.143420e-04
## [76,] 1.121343e-04 1.127521e-04 1.133534e-04 1.139382e-04 1.145065e-04
## [77,] 1.121974e-04 1.128376e-04 1.134612e-04 1.140681e-04 1.146584e-04
## [78,] 1.122492e-04 1.129116e-04 1.135572e-04 1.141860e-04 1.147981e-04
## [79,] 1.122898e-04 1.129742e-04 1.136416e-04 1.142921e-04 1.149258e-04
## [80,] 1.123197e-04 1.130257e-04 1.137147e-04 1.143867e-04 1.150416e-04
## [81,] 1.123390e-04 1.130664e-04 1.137768e-04 1.144699e-04 1.151459e-04
## [82,] 1.123479e-04 1.130966e-04 1.138280e-04 1.145421e-04 1.152390e-04
## [83,] 1.123469e-04 1.131164e-04 1.138687e-04 1.146035e-04 1.153210e-04
## [84,] 1.123360e-04 1.131263e-04 1.138991e-04 1.146544e-04 1.153922e-04
## [85,] 1.123156e-04 1.131263e-04 1.139194e-04 1.146950e-04 1.154529e-04
## [86,] 1.122859e-04 1.131168e-04 1.139300e-04 1.147255e-04 1.155033e-04
## [87,] 1.122472e-04 1.130980e-04 1.139311e-04 1.147463e-04 1.155437e-04
## [88,] 1.121998e-04 1.130703e-04 1.139229e-04 1.147576e-04 1.155743e-04
## [89,] 1.121439e-04 1.130338e-04 1.139057e-04 1.147597e-04 1.155955e-04
## [90,] 1.120798e-04 1.129888e-04 1.138798e-04 1.147527e-04 1.156075e-04
## [91,] 1.120077e-04 1.129356e-04 1.138455e-04 1.147371e-04 1.156104e-04
## [92,] 1.119279e-04 1.128745e-04 1.138029e-04 1.147130e-04 1.156047e-04
## [93,] 1.118406e-04 1.128056e-04 1.137524e-04 1.146807e-04 1.155905e-04
## [94,] 1.117461e-04 1.127293e-04 1.136941e-04 1.146404e-04 1.155681e-04
## [95,] 1.116447e-04 1.126458e-04 1.136284e-04 1.145924e-04 1.155378e-04
## [96,] 1.115366e-04 1.125553e-04 1.135555e-04 1.145370e-04 1.154998e-04
## [97,] 1.114220e-04 1.124581e-04 1.134756e-04 1.144743e-04 1.154543e-04
## [98,] 1.113011e-04 1.123544e-04 1.133890e-04 1.144047e-04 1.154015e-04
## [99,] 1.111743e-04 1.122445e-04 1.132959e-04 1.143284e-04 1.153419e-04
## [100,] 1.110417e-04 1.121285e-04 1.131965e-04 1.142455e-04 1.152754e-04
## [,66] [,67] [,68] [,69] [,70]
## [1,] 6.617294e-05 6.494822e-05 6.372374e-05 6.249996e-05 6.127736e-05
## [2,] 6.707502e-05 6.586835e-05 6.466169e-05 6.345552e-05 6.225030e-05
## [3,] 6.797887e-05 6.679050e-05 6.560193e-05 6.441363e-05 6.322606e-05
## [4,] 6.888418e-05 6.771438e-05 6.654416e-05 6.537399e-05 6.420433e-05
## [5,] 6.979064e-05 6.863967e-05 6.748806e-05 6.633628e-05 6.518479e-05
## [6,] 7.069791e-05 6.956604e-05 6.843331e-05 6.730019e-05 6.616712e-05
## [7,] 7.160568e-05 7.049317e-05 6.937958e-05 6.826537e-05 6.715098e-05
## [8,] 7.251360e-05 7.142071e-05 7.032652e-05 6.923147e-05 6.813602e-05
## [9,] 7.342131e-05 7.234830e-05 7.127377e-05 7.019815e-05 6.912189e-05
## [10,] 7.432845e-05 7.327559e-05 7.222097e-05 7.116504e-05 7.010823e-05
## [11,] 7.523467e-05 7.420221e-05 7.316776e-05 7.213176e-05 7.109465e-05
## [12,] 7.613958e-05 7.512777e-05 7.411374e-05 7.309793e-05 7.208077e-05
## [13,] 7.704279e-05 7.605189e-05 7.505853e-05 7.406316e-05 7.306620e-05
## [14,] 7.794393e-05 7.697418e-05 7.600174e-05 7.502705e-05 7.405053e-05
## [15,] 7.884259e-05 7.789424e-05 7.694297e-05 7.598920e-05 7.503336e-05
## [16,] 7.973836e-05 7.881165e-05 7.788179e-05 7.694919e-05 7.601427e-05
## [17,] 8.063085e-05 7.972602e-05 7.881780e-05 7.790660e-05 7.699283e-05
## [18,] 8.151964e-05 8.063692e-05 7.975057e-05 7.886100e-05 7.796862e-05
## [19,] 8.240430e-05 8.154393e-05 8.067968e-05 7.981197e-05 7.894121e-05
## [20,] 8.328443e-05 8.244662e-05 8.160470e-05 8.075907e-05 7.991014e-05
## [21,] 8.415960e-05 8.334458e-05 8.252520e-05 8.170187e-05 8.087499e-05
## [22,] 8.502938e-05 8.423736e-05 8.344073e-05 8.263992e-05 8.183529e-05
## [23,] 8.589335e-05 8.512453e-05 8.435088e-05 8.357277e-05 8.279062e-05
## [24,] 8.675109e-05 8.600567e-05 8.525518e-05 8.450000e-05 8.374051e-05
## [25,] 8.760216e-05 8.688035e-05 8.615322e-05 8.542114e-05 8.468451e-05
## [26,] 8.844614e-05 8.774812e-05 8.704454e-05 8.633577e-05 8.562218e-05
## [27,] 8.928262e-05 8.860857e-05 8.792872e-05 8.724343e-05 8.655307e-05
## [28,] 9.011117e-05 8.946127e-05 8.880532e-05 8.814368e-05 8.747672e-05
## [29,] 9.093138e-05 9.030580e-05 8.967391e-05 8.903609e-05 8.839270e-05
## [30,] 9.174284e-05 9.114173e-05 9.053407e-05 8.992023e-05 8.930056e-05
## [31,] 9.254515e-05 9.196866e-05 9.138538e-05 9.079567e-05 9.019987e-05
## [32,] 9.333791e-05 9.278618e-05 9.222742e-05 9.166198e-05 9.109020e-05
## [33,] 9.412073e-05 9.359390e-05 9.305979e-05 9.251876e-05 9.197113e-05
## [34,] 9.489323e-05 9.439142e-05 9.388210e-05 9.336559e-05 9.284224e-05
## [35,] 9.565504e-05 9.517837e-05 9.469394e-05 9.420207e-05 9.370312e-05
## [36,] 9.640580e-05 9.595437e-05 9.549494e-05 9.502783e-05 9.455337e-05
## [37,] 9.714516e-05 9.671907e-05 9.628473e-05 9.584247e-05 9.539262e-05
## [38,] 9.787278e-05 9.747211e-05 9.706296e-05 9.664564e-05 9.622047e-05
## [39,] 9.858833e-05 9.821317e-05 9.782928e-05 9.743698e-05 9.703658e-05
## [40,] 9.929150e-05 9.894192e-05 9.858336e-05 9.821615e-05 9.784059e-05
## [41,] 9.998200e-05 9.965804e-05 9.932488e-05 9.898281e-05 9.863215e-05
## [42,] 1.006595e-04 1.003613e-04 1.000535e-04 9.973666e-05 9.941095e-05
## [43,] 1.013238e-04 1.010513e-04 1.007690e-04 1.004774e-04 1.001767e-04
## [44,] 1.019747e-04 1.017278e-04 1.014711e-04 1.012047e-04 1.009290e-04
## [45,] 1.026118e-04 1.023907e-04 1.021595e-04 1.019184e-04 1.016678e-04
## [46,] 1.032349e-04 1.030396e-04 1.028340e-04 1.026182e-04 1.023926e-04
## [47,] 1.038439e-04 1.036744e-04 1.034943e-04 1.033038e-04 1.031032e-04
## [48,] 1.044386e-04 1.042948e-04 1.041402e-04 1.039750e-04 1.037995e-04
## [49,] 1.050188e-04 1.049008e-04 1.047716e-04 1.046317e-04 1.044812e-04
## [50,] 1.055843e-04 1.054920e-04 1.053883e-04 1.052736e-04 1.051482e-04
## [51,] 1.061351e-04 1.060684e-04 1.059902e-04 1.059007e-04 1.058002e-04
## [52,] 1.066709e-04 1.066298e-04 1.065770e-04 1.065126e-04 1.064371e-04
## [53,] 1.071918e-04 1.071762e-04 1.071487e-04 1.071094e-04 1.070587e-04
## [54,] 1.076976e-04 1.077074e-04 1.077052e-04 1.076909e-04 1.076650e-04
## [55,] 1.081882e-04 1.082234e-04 1.082463e-04 1.082571e-04 1.082559e-04
## [56,] 1.086636e-04 1.087242e-04 1.087722e-04 1.088077e-04 1.088312e-04
## [57,] 1.091239e-04 1.092096e-04 1.092826e-04 1.093429e-04 1.093909e-04
## [58,] 1.095689e-04 1.096797e-04 1.097775e-04 1.098626e-04 1.099350e-04
## [59,] 1.099987e-04 1.101345e-04 1.102571e-04 1.103667e-04 1.104634e-04
## [60,] 1.104133e-04 1.105739e-04 1.107212e-04 1.108552e-04 1.109762e-04
## [61,] 1.108128e-04 1.109981e-04 1.111699e-04 1.113282e-04 1.114733e-04
## [62,] 1.111971e-04 1.114071e-04 1.116032e-04 1.117857e-04 1.119547e-04
## [63,] 1.115665e-04 1.118008e-04 1.120212e-04 1.122277e-04 1.124206e-04
## [64,] 1.119209e-04 1.121795e-04 1.124239e-04 1.126543e-04 1.128709e-04
## [65,] 1.122605e-04 1.125432e-04 1.128116e-04 1.130657e-04 1.133057e-04
## [66,] 1.125854e-04 1.128920e-04 1.131841e-04 1.134618e-04 1.137252e-04
## [67,] 1.128956e-04 1.132261e-04 1.135417e-04 1.138428e-04 1.141294e-04
## [68,] 1.131915e-04 1.135455e-04 1.138845e-04 1.142088e-04 1.145184e-04
## [69,] 1.134730e-04 1.138504e-04 1.142127e-04 1.145600e-04 1.148924e-04
## [70,] 1.137404e-04 1.141410e-04 1.145263e-04 1.148964e-04 1.152516e-04
## [71,] 1.139938e-04 1.144174e-04 1.148255e-04 1.152183e-04 1.155959e-04
## [72,] 1.142335e-04 1.146799e-04 1.151106e-04 1.155259e-04 1.159257e-04
## [73,] 1.144595e-04 1.149285e-04 1.153817e-04 1.158192e-04 1.162412e-04
## [74,] 1.146722e-04 1.151636e-04 1.156390e-04 1.160985e-04 1.165424e-04
## [75,] 1.148717e-04 1.153853e-04 1.158827e-04 1.163640e-04 1.168295e-04
## [76,] 1.150583e-04 1.155938e-04 1.161130e-04 1.166160e-04 1.171029e-04
## [77,] 1.152321e-04 1.157893e-04 1.163301e-04 1.168545e-04 1.173627e-04
## [78,] 1.153935e-04 1.159721e-04 1.165342e-04 1.170798e-04 1.176091e-04
## [79,] 1.155425e-04 1.161425e-04 1.167257e-04 1.172923e-04 1.178423e-04
## [80,] 1.156796e-04 1.163006e-04 1.169047e-04 1.174920e-04 1.180626e-04
## [81,] 1.158048e-04 1.164466e-04 1.170714e-04 1.176792e-04 1.182702e-04
## [82,] 1.159186e-04 1.165809e-04 1.172261e-04 1.178542e-04 1.184653e-04
## [83,] 1.160210e-04 1.167037e-04 1.173691e-04 1.180173e-04 1.186482e-04
## [84,] 1.161125e-04 1.168153e-04 1.175006e-04 1.181686e-04 1.188192e-04
## [85,] 1.161931e-04 1.169158e-04 1.176208e-04 1.183084e-04 1.189785e-04
## [86,] 1.162633e-04 1.170055e-04 1.177301e-04 1.184370e-04 1.191263e-04
## [87,] 1.163232e-04 1.170848e-04 1.178286e-04 1.185546e-04 1.192629e-04
## [88,] 1.163731e-04 1.171539e-04 1.179167e-04 1.186615e-04 1.193885e-04
## [89,] 1.164133e-04 1.172129e-04 1.179945e-04 1.187580e-04 1.195035e-04
## [90,] 1.164440e-04 1.172623e-04 1.180624e-04 1.188443e-04 1.196081e-04
## [91,] 1.164655e-04 1.173022e-04 1.181206e-04 1.189206e-04 1.197024e-04
## [92,] 1.164780e-04 1.173329e-04 1.181693e-04 1.189873e-04 1.197869e-04
## [93,] 1.164819e-04 1.173546e-04 1.182089e-04 1.190446e-04 1.198617e-04
## [94,] 1.164772e-04 1.173677e-04 1.182395e-04 1.190927e-04 1.199272e-04
## [95,] 1.164644e-04 1.173723e-04 1.182615e-04 1.191318e-04 1.199834e-04
## [96,] 1.164437e-04 1.173688e-04 1.182750e-04 1.191624e-04 1.200308e-04
## [97,] 1.164153e-04 1.173573e-04 1.182804e-04 1.191845e-04 1.200696e-04
## [98,] 1.163794e-04 1.173381e-04 1.182778e-04 1.191985e-04 1.201000e-04
## [99,] 1.163363e-04 1.173115e-04 1.182676e-04 1.192045e-04 1.201222e-04
## [100,] 1.162862e-04 1.172777e-04 1.182499e-04 1.192029e-04 1.201365e-04
## [,71] [,72] [,73] [,74] [,75]
## [1,] 6.005638e-05 5.883748e-05 5.762107e-05 5.640758e-05 5.519742e-05
## [2,] 6.104649e-05 5.984452e-05 5.864483e-05 5.744783e-05 5.625393e-05
## [3,] 6.203967e-05 6.085490e-05 5.967218e-05 5.849191e-05 5.731451e-05
## [4,] 6.303562e-05 6.186830e-05 6.070279e-05 5.953952e-05 5.837887e-05
## [5,] 6.403401e-05 6.288440e-05 6.173637e-05 6.059033e-05 5.944669e-05
## [6,] 6.503454e-05 6.390288e-05 6.277258e-05 6.164403e-05 6.051764e-05
## [7,] 6.603685e-05 6.492341e-05 6.381108e-05 6.270027e-05 6.159138e-05
## [8,] 6.704060e-05 6.594563e-05 6.485153e-05 6.375871e-05 6.266756e-05
## [9,] 6.804543e-05 6.696918e-05 6.589356e-05 6.481897e-05 6.374582e-05
## [10,] 6.905097e-05 6.799369e-05 6.693680e-05 6.588070e-05 6.482578e-05
## [11,] 7.005685e-05 6.901879e-05 6.798087e-05 6.694350e-05 6.590705e-05
## [12,] 7.106268e-05 7.004409e-05 6.902539e-05 6.800698e-05 6.698926e-05
## [13,] 7.206807e-05 7.106918e-05 7.006994e-05 6.907074e-05 6.807198e-05
## [14,] 7.307260e-05 7.209366e-05 7.111412e-05 7.013437e-05 6.915480e-05
## [15,] 7.407586e-05 7.311711e-05 7.215751e-05 7.119745e-05 7.023730e-05
## [16,] 7.507745e-05 7.413912e-05 7.319969e-05 7.225954e-05 7.131905e-05
## [17,] 7.607692e-05 7.515924e-05 7.424021e-05 7.332021e-05 7.239961e-05
## [18,] 7.707384e-05 7.617705e-05 7.527865e-05 7.437901e-05 7.347852e-05
## [19,] 7.806778e-05 7.719210e-05 7.631455e-05 7.543550e-05 7.455534e-05
## [20,] 7.905830e-05 7.820395e-05 7.734746e-05 7.648922e-05 7.562960e-05
## [21,] 8.004494e-05 7.921213e-05 7.837692e-05 7.753970e-05 7.670083e-05
## [22,] 8.102726e-05 8.021619e-05 7.940248e-05 7.858648e-05 7.776857e-05
## [23,] 8.200479e-05 8.121568e-05 8.042366e-05 7.962909e-05 7.883234e-05
## [24,] 8.297709e-05 8.221013e-05 8.144000e-05 8.066705e-05 7.989166e-05
## [25,] 8.394370e-05 8.319908e-05 8.245103e-05 8.169990e-05 8.094606e-05
## [26,] 8.490416e-05 8.418207e-05 8.345628e-05 8.272715e-05 8.199504e-05
## [27,] 8.585802e-05 8.515864e-05 8.445529e-05 8.374834e-05 8.303813e-05
## [28,] 8.680481e-05 8.612831e-05 8.544758e-05 8.476298e-05 8.407485e-05
## [29,] 8.774410e-05 8.709065e-05 8.643270e-05 8.577060e-05 8.510472e-05
## [30,] 8.867543e-05 8.804518e-05 8.741017e-05 8.677074e-05 8.612725e-05
## [31,] 8.959835e-05 8.899146e-05 8.837954e-05 8.776293e-05 8.714199e-05
## [32,] 9.051244e-05 8.992904e-05 8.934035e-05 8.874671e-05 8.814845e-05
## [33,] 9.141726e-05 9.085749e-05 9.029216e-05 8.972162e-05 8.914619e-05
## [34,] 9.231239e-05 9.177637e-05 9.123453e-05 9.068721e-05 9.013473e-05
## [35,] 9.319740e-05 9.268526e-05 9.216703e-05 9.164304e-05 9.111363e-05
## [36,] 9.407190e-05 9.358374e-05 9.308923e-05 9.258869e-05 9.208245e-05
## [37,] 9.493549e-05 9.447141e-05 9.400071e-05 9.352372e-05 9.304076e-05
## [38,] 9.578778e-05 9.534787e-05 9.490108e-05 9.444773e-05 9.398814e-05
## [39,] 9.662840e-05 9.621274e-05 9.578994e-05 9.536031e-05 9.492417e-05
## [40,] 9.745698e-05 9.706566e-05 9.666692e-05 9.626109e-05 9.584847e-05
## [41,] 9.827319e-05 9.790625e-05 9.753164e-05 9.714967e-05 9.676064e-05
## [42,] 9.907669e-05 9.873419e-05 9.838376e-05 9.802570e-05 9.766032e-05
## [43,] 9.986716e-05 9.954914e-05 9.922293e-05 9.888883e-05 9.854715e-05
## [44,] 1.006443e-04 1.003508e-04 1.000488e-04 9.973874e-05 9.942078e-05
## [45,] 1.014078e-04 1.011389e-04 1.008612e-04 1.005751e-04 1.002809e-04
## [46,] 1.021574e-04 1.019130e-04 1.016597e-04 1.013976e-04 1.011272e-04
## [47,] 1.028929e-04 1.026731e-04 1.024440e-04 1.022060e-04 1.019594e-04
## [48,] 1.036140e-04 1.034187e-04 1.032140e-04 1.030000e-04 1.027772e-04
## [49,] 1.043205e-04 1.041498e-04 1.039693e-04 1.037794e-04 1.035803e-04
## [50,] 1.050122e-04 1.048660e-04 1.047098e-04 1.045439e-04 1.043685e-04
## [51,] 1.056889e-04 1.055672e-04 1.054352e-04 1.052933e-04 1.051417e-04
## [52,] 1.063505e-04 1.062532e-04 1.061454e-04 1.060274e-04 1.058995e-04
## [53,] 1.069968e-04 1.069239e-04 1.068402e-04 1.067462e-04 1.066419e-04
## [54,] 1.076276e-04 1.075791e-04 1.075195e-04 1.074493e-04 1.073686e-04
## [55,] 1.082430e-04 1.082187e-04 1.081831e-04 1.081367e-04 1.080795e-04
## [56,] 1.088427e-04 1.088426e-04 1.088310e-04 1.088082e-04 1.087745e-04
## [57,] 1.094268e-04 1.094507e-04 1.094630e-04 1.094638e-04 1.094535e-04
## [58,] 1.099951e-04 1.100430e-04 1.100790e-04 1.101034e-04 1.101164e-04
## [59,] 1.105476e-04 1.106194e-04 1.106791e-04 1.107269e-04 1.107631e-04
## [60,] 1.110844e-04 1.111800e-04 1.112632e-04 1.113343e-04 1.113935e-04
## [61,] 1.116053e-04 1.117246e-04 1.118313e-04 1.119256e-04 1.120078e-04
## [62,] 1.121105e-04 1.122533e-04 1.123833e-04 1.125007e-04 1.126057e-04
## [63,] 1.126000e-04 1.127662e-04 1.129193e-04 1.130597e-04 1.131874e-04
## [64,] 1.130738e-04 1.132632e-04 1.134394e-04 1.136025e-04 1.137529e-04
## [65,] 1.135319e-04 1.137445e-04 1.139435e-04 1.141294e-04 1.143022e-04
## [66,] 1.139746e-04 1.142101e-04 1.144319e-04 1.146402e-04 1.148353e-04
## [67,] 1.144018e-04 1.146600e-04 1.149044e-04 1.151351e-04 1.153523e-04
## [68,] 1.148136e-04 1.150945e-04 1.153613e-04 1.156142e-04 1.158534e-04
## [69,] 1.152103e-04 1.155136e-04 1.158026e-04 1.160776e-04 1.163386e-04
## [70,] 1.155918e-04 1.159174e-04 1.162286e-04 1.165254e-04 1.168081e-04
## [71,] 1.159585e-04 1.163062e-04 1.166392e-04 1.169577e-04 1.172618e-04
## [72,] 1.163104e-04 1.166800e-04 1.170347e-04 1.173747e-04 1.177001e-04
## [73,] 1.166477e-04 1.170390e-04 1.174152e-04 1.177765e-04 1.181231e-04
## [74,] 1.169706e-04 1.173834e-04 1.177809e-04 1.181633e-04 1.185308e-04
## [75,] 1.172793e-04 1.177134e-04 1.181320e-04 1.185354e-04 1.189236e-04
## [76,] 1.175739e-04 1.180291e-04 1.184687e-04 1.188928e-04 1.193015e-04
## [77,] 1.178547e-04 1.183308e-04 1.187911e-04 1.192357e-04 1.196648e-04
## [78,] 1.181220e-04 1.186188e-04 1.190995e-04 1.195645e-04 1.200137e-04
## [79,] 1.183758e-04 1.188931e-04 1.193941e-04 1.198792e-04 1.203484e-04
## [80,] 1.186165e-04 1.191540e-04 1.196752e-04 1.201801e-04 1.206690e-04
## [81,] 1.188443e-04 1.194019e-04 1.199429e-04 1.204675e-04 1.209759e-04
## [82,] 1.190594e-04 1.196368e-04 1.201974e-04 1.207416e-04 1.212693e-04
## [83,] 1.192621e-04 1.198591e-04 1.204391e-04 1.210025e-04 1.215493e-04
## [84,] 1.194526e-04 1.200689e-04 1.206682e-04 1.212506e-04 1.218163e-04
## [85,] 1.196312e-04 1.202666e-04 1.208849e-04 1.214861e-04 1.220704e-04
## [86,] 1.197980e-04 1.204524e-04 1.210894e-04 1.217092e-04 1.223120e-04
## [87,] 1.199535e-04 1.206265e-04 1.212820e-04 1.219203e-04 1.225412e-04
## [88,] 1.200977e-04 1.207892e-04 1.214631e-04 1.221194e-04 1.227584e-04
## [89,] 1.202311e-04 1.209408e-04 1.216327e-04 1.223070e-04 1.229638e-04
## [90,] 1.203538e-04 1.210815e-04 1.217913e-04 1.224832e-04 1.231576e-04
## [91,] 1.204660e-04 1.212115e-04 1.219389e-04 1.226484e-04 1.233401e-04
## [92,] 1.205682e-04 1.213312e-04 1.220760e-04 1.228028e-04 1.235115e-04
## [93,] 1.206605e-04 1.214408e-04 1.222028e-04 1.229465e-04 1.236722e-04
## [94,] 1.207431e-04 1.215405e-04 1.223194e-04 1.230800e-04 1.238224e-04
## [95,] 1.208163e-04 1.216306e-04 1.224263e-04 1.232034e-04 1.239622e-04
## [96,] 1.208805e-04 1.217114e-04 1.225235e-04 1.233171e-04 1.240921e-04
## [97,] 1.209358e-04 1.217831e-04 1.226115e-04 1.234212e-04 1.242122e-04
## [98,] 1.209824e-04 1.218459e-04 1.226904e-04 1.235160e-04 1.243229e-04
## [99,] 1.210207e-04 1.219001e-04 1.227605e-04 1.236018e-04 1.244242e-04
## [100,] 1.210509e-04 1.219461e-04 1.228220e-04 1.236788e-04 1.245166e-04
## [,76] [,77] [,78] [,79] [,80]
## [1,] 5.399098e-05 5.278864e-05 5.159076e-05 5.039770e-05 4.920980e-05
## [2,] 5.506351e-05 5.387696e-05 5.269464e-05 5.151692e-05 5.034411e-05
## [3,] 5.614037e-05 5.496986e-05 5.380334e-05 5.264118e-05 5.148372e-05
## [4,] 5.722124e-05 5.606702e-05 5.491655e-05 5.377020e-05 5.262830e-05
## [5,] 5.830583e-05 5.716813e-05 5.603395e-05 5.490364e-05 5.377755e-05
## [6,] 5.939379e-05 5.827286e-05 5.715521e-05 5.604119e-05 5.493115e-05
## [7,] 6.048479e-05 5.938087e-05 5.827999e-05 5.718250e-05 5.608873e-05
## [8,] 6.157847e-05 6.049181e-05 5.940794e-05 5.832721e-05 5.724996e-05
## [9,] 6.267447e-05 6.160531e-05 6.053869e-05 5.947496e-05 5.841446e-05
## [10,] 6.377242e-05 6.272099e-05 6.167186e-05 6.062537e-05 5.958186e-05
## [11,] 6.487192e-05 6.383847e-05 6.280707e-05 6.177805e-05 6.075176e-05
## [12,] 6.597259e-05 6.495736e-05 6.394391e-05 6.293260e-05 6.192375e-05
## [13,] 6.707402e-05 6.607723e-05 6.508198e-05 6.408860e-05 6.309743e-05
## [14,] 6.817578e-05 6.719767e-05 6.622084e-05 6.524563e-05 6.427237e-05
## [15,] 6.927745e-05 6.831826e-05 6.736008e-05 6.640325e-05 6.544812e-05
## [16,] 7.037860e-05 6.943855e-05 6.849924e-05 6.756103e-05 6.662425e-05
## [17,] 7.147878e-05 7.055809e-05 6.963788e-05 6.871851e-05 6.780029e-05
## [18,] 7.257754e-05 7.167643e-05 7.077554e-05 6.987522e-05 6.897579e-05
## [19,] 7.367442e-05 7.279311e-05 7.191176e-05 7.103070e-05 7.015026e-05
## [20,] 7.476896e-05 7.390766e-05 7.304605e-05 7.218446e-05 7.132323e-05
## [21,] 7.586068e-05 7.501961e-05 7.417794e-05 7.333603e-05 7.249421e-05
## [22,] 7.694912e-05 7.612846e-05 7.530695e-05 7.448492e-05 7.366270e-05
## [23,] 7.803378e-05 7.723374e-05 7.643258e-05 7.563063e-05 7.482821e-05
## [24,] 7.911419e-05 7.833496e-05 7.755434e-05 7.677266e-05 7.599023e-05
## [25,] 8.018985e-05 7.943163e-05 7.867174e-05 7.791050e-05 7.714825e-05
## [26,] 8.126029e-05 8.052326e-05 7.978427e-05 7.904367e-05 7.830177e-05
## [27,] 8.232502e-05 8.160934e-05 8.089144e-05 8.017164e-05 7.945027e-05
## [28,] 8.338354e-05 8.268939e-05 8.199274e-05 8.129392e-05 8.059324e-05
## [29,] 8.443537e-05 8.376292e-05 8.308768e-05 8.240999e-05 8.173016e-05
## [30,] 8.548004e-05 8.482943e-05 8.417576e-05 8.351936e-05 8.286054e-05
## [31,] 8.651704e-05 8.588843e-05 8.525648e-05 8.462152e-05 8.398385e-05
## [32,] 8.754592e-05 8.693945e-05 8.632936e-05 8.571597e-05 8.509960e-05
## [33,] 8.856620e-05 8.798200e-05 8.739390e-05 8.680222e-05 8.620728e-05
## [34,] 8.957742e-05 8.901561e-05 8.844963e-05 8.787978e-05 8.730639e-05
## [35,] 9.057911e-05 9.003982e-05 8.949607e-05 8.894818e-05 8.839646e-05
## [36,] 9.157083e-05 9.105416e-05 9.053276e-05 9.000693e-05 8.947699e-05
## [37,] 9.255215e-05 9.205820e-05 9.155924e-05 9.105558e-05 9.054752e-05
## [38,] 9.352262e-05 9.305149e-05 9.257507e-05 9.209367e-05 9.160758e-05
## [39,] 9.448183e-05 9.403361e-05 9.357981e-05 9.312075e-05 9.265673e-05
## [40,] 9.542938e-05 9.500413e-05 9.457303e-05 9.413639e-05 9.369451e-05
## [41,] 9.636487e-05 9.596267e-05 9.555434e-05 9.514018e-05 9.472050e-05
## [42,] 9.728792e-05 9.690882e-05 9.652331e-05 9.613170e-05 9.573429e-05
## [43,] 9.819817e-05 9.784222e-05 9.747958e-05 9.711057e-05 9.673547e-05
## [44,] 9.909527e-05 9.876250e-05 9.842278e-05 9.807640e-05 9.772366e-05
## [45,] 9.997888e-05 9.966933e-05 9.935255e-05 9.902884e-05 9.869849e-05
## [46,] 1.008487e-04 1.005624e-04 1.002686e-04 9.996754e-05 9.965960e-05
## [47,] 1.017044e-04 1.014413e-04 1.011705e-04 1.008922e-04 1.006067e-04
## [48,] 1.025457e-04 1.023059e-04 1.020580e-04 1.018024e-04 1.015394e-04
## [49,] 1.033723e-04 1.031558e-04 1.029309e-04 1.026980e-04 1.024574e-04
## [50,] 1.041841e-04 1.039907e-04 1.037888e-04 1.035786e-04 1.033604e-04
## [51,] 1.049807e-04 1.048106e-04 1.046316e-04 1.044441e-04 1.042483e-04
## [52,] 1.057620e-04 1.056150e-04 1.054590e-04 1.052941e-04 1.051206e-04
## [53,] 1.065277e-04 1.064039e-04 1.062707e-04 1.061284e-04 1.059773e-04
## [54,] 1.072778e-04 1.071770e-04 1.070666e-04 1.069469e-04 1.068181e-04
## [55,] 1.080119e-04 1.079342e-04 1.078466e-04 1.077494e-04 1.076428e-04
## [56,] 1.087301e-04 1.086754e-04 1.086104e-04 1.085357e-04 1.084513e-04
## [57,] 1.094322e-04 1.094003e-04 1.093580e-04 1.093056e-04 1.092433e-04
## [58,] 1.101181e-04 1.101090e-04 1.100893e-04 1.100591e-04 1.100189e-04
## [59,] 1.107878e-04 1.108014e-04 1.108041e-04 1.107961e-04 1.107778e-04
## [60,] 1.114411e-04 1.114773e-04 1.115023e-04 1.115165e-04 1.115200e-04
## [61,] 1.120781e-04 1.121367e-04 1.121840e-04 1.122202e-04 1.122455e-04
## [62,] 1.126986e-04 1.127797e-04 1.128491e-04 1.129071e-04 1.129541e-04
## [63,] 1.133028e-04 1.134061e-04 1.134975e-04 1.135774e-04 1.136458e-04
## [64,] 1.138906e-04 1.140161e-04 1.141294e-04 1.142309e-04 1.143207e-04
## [65,] 1.144621e-04 1.146095e-04 1.147446e-04 1.148676e-04 1.149787e-04
## [66,] 1.150173e-04 1.151866e-04 1.153433e-04 1.154877e-04 1.156199e-04
## [67,] 1.155563e-04 1.157473e-04 1.159254e-04 1.160911e-04 1.162444e-04
## [68,] 1.160792e-04 1.162917e-04 1.164912e-04 1.166779e-04 1.168520e-04
## [69,] 1.165860e-04 1.168199e-04 1.170405e-04 1.172482e-04 1.174430e-04
## [70,] 1.170768e-04 1.173320e-04 1.175736e-04 1.178020e-04 1.180175e-04
## [71,] 1.175519e-04 1.178281e-04 1.180906e-04 1.183396e-04 1.185754e-04
## [72,] 1.180113e-04 1.183083e-04 1.185915e-04 1.188610e-04 1.191170e-04
## [73,] 1.184551e-04 1.187729e-04 1.190765e-04 1.193663e-04 1.196424e-04
## [74,] 1.188836e-04 1.192219e-04 1.195459e-04 1.198557e-04 1.201518e-04
## [75,] 1.192969e-04 1.196555e-04 1.199996e-04 1.203294e-04 1.206451e-04
## [76,] 1.196952e-04 1.200740e-04 1.204380e-04 1.207875e-04 1.211228e-04
## [77,] 1.200787e-04 1.204774e-04 1.208611e-04 1.212302e-04 1.215848e-04
## [78,] 1.204475e-04 1.208659e-04 1.212693e-04 1.216577e-04 1.220315e-04
## [79,] 1.208019e-04 1.212399e-04 1.216626e-04 1.220702e-04 1.224630e-04
## [80,] 1.211421e-04 1.215995e-04 1.220413e-04 1.224679e-04 1.228794e-04
## [81,] 1.214683e-04 1.219448e-04 1.224057e-04 1.228510e-04 1.232811e-04
## [82,] 1.217808e-04 1.222762e-04 1.227558e-04 1.232198e-04 1.236682e-04
## [83,] 1.220797e-04 1.225939e-04 1.230921e-04 1.235744e-04 1.240410e-04
## [84,] 1.223654e-04 1.228981e-04 1.234146e-04 1.239151e-04 1.243997e-04
## [85,] 1.226380e-04 1.231891e-04 1.237237e-04 1.242421e-04 1.247446e-04
## [86,] 1.228979e-04 1.234670e-04 1.240196e-04 1.245558e-04 1.250758e-04
## [87,] 1.231452e-04 1.237322e-04 1.243025e-04 1.248562e-04 1.253936e-04
## [88,] 1.233802e-04 1.239849e-04 1.245727e-04 1.251438e-04 1.256983e-04
## [89,] 1.236032e-04 1.242253e-04 1.248304e-04 1.254186e-04 1.259902e-04
## [90,] 1.238144e-04 1.244538e-04 1.250760e-04 1.256811e-04 1.262694e-04
## [91,] 1.240140e-04 1.246705e-04 1.253095e-04 1.259314e-04 1.265362e-04
## [92,] 1.242025e-04 1.248757e-04 1.255314e-04 1.261698e-04 1.267910e-04
## [93,] 1.243799e-04 1.250697e-04 1.257419e-04 1.263966e-04 1.270339e-04
## [94,] 1.245466e-04 1.252528e-04 1.259412e-04 1.266119e-04 1.272652e-04
## [95,] 1.247028e-04 1.254252e-04 1.261296e-04 1.268162e-04 1.274852e-04
## [96,] 1.248487e-04 1.255871e-04 1.263074e-04 1.270096e-04 1.276941e-04
## [97,] 1.249848e-04 1.257389e-04 1.264747e-04 1.271924e-04 1.278922e-04
## [98,] 1.251110e-04 1.258807e-04 1.266319e-04 1.273649e-04 1.280798e-04
## [99,] 1.252279e-04 1.260128e-04 1.267793e-04 1.275273e-04 1.282571e-04
## [100,] 1.253355e-04 1.261356e-04 1.269170e-04 1.276798e-04 1.284244e-04
## [,81] [,82] [,83] [,84] [,85]
## [1,] 4.802739e-05 4.685077e-05 4.568025e-05 4.451611e-05 4.335862e-05
## [2,] 4.917657e-05 4.801458e-05 4.685846e-05 4.570849e-05 4.456494e-05
## [3,] 5.033127e-05 4.918414e-05 4.804265e-05 4.690708e-05 4.577769e-05
## [4,] 5.149118e-05 5.035916e-05 4.923253e-05 4.811157e-05 4.699657e-05
## [5,] 5.265600e-05 5.153931e-05 5.042776e-05 4.932166e-05 4.822127e-05
## [6,] 5.382540e-05 5.272426e-05 5.162803e-05 5.053701e-05 4.945145e-05
## [7,] 5.499902e-05 5.391368e-05 5.283300e-05 5.175727e-05 5.068677e-05
## [8,] 5.617652e-05 5.510720e-05 5.404229e-05 5.298210e-05 5.192688e-05
## [9,] 5.735752e-05 5.630445e-05 5.525555e-05 5.421111e-05 5.317141e-05
## [10,] 5.854165e-05 5.750507e-05 5.647240e-05 5.544393e-05 5.441996e-05
## [11,] 5.972852e-05 5.870864e-05 5.769242e-05 5.668016e-05 5.567214e-05
## [12,] 6.091770e-05 5.991476e-05 5.891523e-05 5.791939e-05 5.692754e-05
## [13,] 6.210880e-05 6.112302e-05 6.014039e-05 5.916120e-05 5.818573e-05
## [14,] 6.330138e-05 6.233298e-05 6.136747e-05 6.040515e-05 5.944628e-05
## [15,] 6.449500e-05 6.354421e-05 6.259604e-05 6.165079e-05 6.070875e-05
## [16,] 6.568921e-05 6.475624e-05 6.382563e-05 6.289768e-05 6.197266e-05
## [17,] 6.688356e-05 6.596862e-05 6.505578e-05 6.414534e-05 6.323756e-05
## [18,] 6.807757e-05 6.718088e-05 6.628602e-05 6.539329e-05 6.450295e-05
## [19,] 6.927077e-05 6.839254e-05 6.751587e-05 6.664105e-05 6.576836e-05
## [20,] 7.046267e-05 6.960310e-05 6.874482e-05 6.788812e-05 6.703328e-05
## [21,] 7.165278e-05 7.081207e-05 6.997238e-05 6.913399e-05 6.829720e-05
## [22,] 7.284061e-05 7.201896e-05 7.119805e-05 7.037817e-05 6.955961e-05
## [23,] 7.402564e-05 7.322324e-05 7.242130e-05 7.162012e-05 7.081998e-05
## [24,] 7.520737e-05 7.442441e-05 7.364163e-05 7.285933e-05 7.207780e-05
## [25,] 7.638529e-05 7.562195e-05 7.485851e-05 7.409527e-05 7.333252e-05
## [26,] 7.755889e-05 7.681533e-05 7.607141e-05 7.532741e-05 7.458361e-05
## [27,] 7.872763e-05 7.800405e-05 7.727981e-05 7.655521e-05 7.583054e-05
## [28,] 7.989101e-05 7.918756e-05 7.848317e-05 7.777814e-05 7.707275e-05
## [29,] 8.104851e-05 8.036535e-05 7.968097e-05 7.899566e-05 7.830972e-05
## [30,] 8.219961e-05 8.153689e-05 8.087267e-05 8.020724e-05 7.954088e-05
## [31,] 8.334380e-05 8.270166e-05 8.205775e-05 8.141233e-05 8.076571e-05
## [32,] 8.448056e-05 8.385915e-05 8.323567e-05 8.261042e-05 8.198367e-05
## [33,] 8.560938e-05 8.500883e-05 8.440593e-05 8.380096e-05 8.319422e-05
## [34,] 8.672977e-05 8.615020e-05 8.556800e-05 8.498345e-05 8.439683e-05
## [35,] 8.784122e-05 8.728275e-05 8.672137e-05 8.615734e-05 8.559097e-05
## [36,] 8.894325e-05 8.840600e-05 8.786553e-05 8.732215e-05 8.677612e-05
## [37,] 9.003537e-05 8.951944e-05 8.900000e-05 8.847735e-05 8.795178e-05
## [38,] 9.111713e-05 9.062260e-05 9.012428e-05 8.962247e-05 8.911745e-05
## [39,] 9.218805e-05 9.171501e-05 9.123790e-05 9.075701e-05 9.027262e-05
## [40,] 9.324768e-05 9.279621e-05 9.234039e-05 9.188049e-05 9.141682e-05
## [41,] 9.429560e-05 9.386576e-05 9.343129e-05 9.299247e-05 9.254957e-05
## [42,] 9.533137e-05 9.492323e-05 9.451018e-05 9.409248e-05 9.367043e-05
## [43,] 9.635458e-05 9.596820e-05 9.557661e-05 9.518010e-05 9.477895e-05
## [44,] 9.736485e-05 9.700026e-05 9.663019e-05 9.625490e-05 9.587470e-05
## [45,] 9.836179e-05 9.801903e-05 9.767050e-05 9.731649e-05 9.695726e-05
## [46,] 9.934504e-05 9.902414e-05 9.869718e-05 9.836446e-05 9.802625e-05
## [47,] 1.003143e-04 1.000152e-04 9.970986e-05 9.939845e-05 9.908127e-05
## [48,] 1.012691e-04 1.009920e-04 1.007082e-04 1.004181e-04 1.001220e-04
## [49,] 1.022093e-04 1.019540e-04 1.016919e-04 1.014231e-04 1.011480e-04
## [50,] 1.031345e-04 1.029011e-04 1.026605e-04 1.024131e-04 1.021591e-04
## [51,] 1.040444e-04 1.038329e-04 1.036140e-04 1.033878e-04 1.031548e-04
## [52,] 1.049389e-04 1.047492e-04 1.045518e-04 1.043470e-04 1.041350e-04
## [53,] 1.058177e-04 1.056498e-04 1.054739e-04 1.052903e-04 1.050993e-04
## [54,] 1.066805e-04 1.065343e-04 1.063800e-04 1.062176e-04 1.060475e-04
## [55,] 1.075272e-04 1.074027e-04 1.072698e-04 1.071286e-04 1.069794e-04
## [56,] 1.083575e-04 1.082548e-04 1.081432e-04 1.080231e-04 1.078948e-04
## [57,] 1.091715e-04 1.090903e-04 1.090000e-04 1.089010e-04 1.087935e-04
## [58,] 1.099688e-04 1.099091e-04 1.098401e-04 1.097621e-04 1.096752e-04
## [59,] 1.107494e-04 1.107111e-04 1.106633e-04 1.106062e-04 1.105400e-04
## [60,] 1.115132e-04 1.114963e-04 1.114695e-04 1.114332e-04 1.113876e-04
## [61,] 1.122601e-04 1.122645e-04 1.122587e-04 1.122431e-04 1.122180e-04
## [62,] 1.129901e-04 1.130156e-04 1.130308e-04 1.130358e-04 1.130311e-04
## [63,] 1.137032e-04 1.137497e-04 1.137856e-04 1.138112e-04 1.138268e-04
## [64,] 1.143992e-04 1.144667e-04 1.145233e-04 1.145693e-04 1.146050e-04
## [65,] 1.150783e-04 1.151665e-04 1.152437e-04 1.153100e-04 1.153658e-04
## [66,] 1.157404e-04 1.158493e-04 1.159469e-04 1.160334e-04 1.161091e-04
## [67,] 1.163856e-04 1.165150e-04 1.166329e-04 1.167395e-04 1.168350e-04
## [68,] 1.170139e-04 1.171637e-04 1.173017e-04 1.174282e-04 1.175435e-04
## [69,] 1.176254e-04 1.177955e-04 1.179535e-04 1.180998e-04 1.182346e-04
## [70,] 1.182201e-04 1.184103e-04 1.185882e-04 1.187542e-04 1.189083e-04
## [71,] 1.187983e-04 1.190084e-04 1.192060e-04 1.193915e-04 1.195649e-04
## [72,] 1.193599e-04 1.195898e-04 1.198070e-04 1.200118e-04 1.202043e-04
## [73,] 1.199051e-04 1.201547e-04 1.203913e-04 1.206152e-04 1.208267e-04
## [74,] 1.204341e-04 1.207031e-04 1.209590e-04 1.212019e-04 1.214322e-04
## [75,] 1.209470e-04 1.212353e-04 1.215102e-04 1.217720e-04 1.220209e-04
## [76,] 1.214440e-04 1.217514e-04 1.220452e-04 1.223256e-04 1.225930e-04
## [77,] 1.219252e-04 1.222515e-04 1.225640e-04 1.228630e-04 1.231487e-04
## [78,] 1.223908e-04 1.227359e-04 1.230669e-04 1.233842e-04 1.236881e-04
## [79,] 1.228410e-04 1.232047e-04 1.235541e-04 1.238896e-04 1.242113e-04
## [80,] 1.232761e-04 1.236581e-04 1.240257e-04 1.243792e-04 1.247187e-04
## [81,] 1.236962e-04 1.240964e-04 1.244820e-04 1.248532e-04 1.252103e-04
## [82,] 1.241015e-04 1.245197e-04 1.249231e-04 1.253119e-04 1.256865e-04
## [83,] 1.244923e-04 1.249283e-04 1.253493e-04 1.257556e-04 1.261473e-04
## [84,] 1.248688e-04 1.253224e-04 1.257608e-04 1.261843e-04 1.265931e-04
## [85,] 1.252312e-04 1.257022e-04 1.261579e-04 1.265985e-04 1.270241e-04
## [86,] 1.255798e-04 1.260681e-04 1.265408e-04 1.269982e-04 1.274405e-04
## [87,] 1.259148e-04 1.264201e-04 1.269097e-04 1.273837e-04 1.278425e-04
## [88,] 1.262365e-04 1.267586e-04 1.272648e-04 1.277554e-04 1.282304e-04
## [89,] 1.265452e-04 1.270839e-04 1.276065e-04 1.281133e-04 1.286045e-04
## [90,] 1.268410e-04 1.273961e-04 1.279350e-04 1.284579e-04 1.289649e-04
## [91,] 1.271242e-04 1.276956e-04 1.282505e-04 1.287893e-04 1.293120e-04
## [92,] 1.273951e-04 1.279825e-04 1.285533e-04 1.291077e-04 1.296460e-04
## [93,] 1.276540e-04 1.282572e-04 1.288437e-04 1.294136e-04 1.299672e-04
## [94,] 1.279011e-04 1.285199e-04 1.291218e-04 1.297071e-04 1.302758e-04
## [95,] 1.281367e-04 1.287709e-04 1.293881e-04 1.299884e-04 1.305721e-04
## [96,] 1.283610e-04 1.290104e-04 1.296427e-04 1.302579e-04 1.308563e-04
## [97,] 1.285743e-04 1.292387e-04 1.298858e-04 1.305158e-04 1.311288e-04
## [98,] 1.287768e-04 1.294561e-04 1.301179e-04 1.307623e-04 1.313897e-04
## [99,] 1.289689e-04 1.296628e-04 1.303390e-04 1.309978e-04 1.316393e-04
## [100,] 1.291507e-04 1.298590e-04 1.305495e-04 1.312224e-04 1.318780e-04
## [,86] [,87] [,88] [,89] [,90]
## [1,] 4.220805e-05 4.106462e-05 3.992857e-05 3.880013e-05 3.767949e-05
## [2,] 4.342807e-05 4.229812e-05 4.117533e-05 4.005991e-05 3.895207e-05
## [3,] 4.465475e-05 4.353850e-05 4.242917e-05 4.132700e-05 4.023217e-05
## [4,] 4.588778e-05 4.478545e-05 4.368981e-05 4.260108e-05 4.151948e-05
## [5,] 4.712685e-05 4.603865e-05 4.495692e-05 4.388186e-05 4.281370e-05
## [6,] 4.837163e-05 4.729779e-05 4.623017e-05 4.516900e-05 4.411448e-05
## [7,] 4.962177e-05 4.856251e-05 4.750923e-05 4.646215e-05 4.542149e-05
## [8,] 5.087692e-05 4.983245e-05 4.879372e-05 4.776096e-05 4.673437e-05
## [9,] 5.213670e-05 5.110725e-05 5.008328e-05 4.906504e-05 4.805274e-05
## [10,] 5.340073e-05 5.238651e-05 5.137753e-05 5.037403e-05 4.937622e-05
## [11,] 5.466861e-05 5.366983e-05 5.267605e-05 5.168750e-05 5.070439e-05
## [12,] 5.593992e-05 5.495681e-05 5.397844e-05 5.300504e-05 5.203685e-05
## [13,] 5.721425e-05 5.624701e-05 5.528426e-05 5.432624e-05 5.337316e-05
## [14,] 5.849115e-05 5.754000e-05 5.659308e-05 5.565063e-05 5.471287e-05
## [15,] 5.977017e-05 5.883532e-05 5.790444e-05 5.697777e-05 5.605554e-05
## [16,] 6.105085e-05 6.013250e-05 5.921787e-05 5.830718e-05 5.740068e-05
## [17,] 6.233272e-05 6.143108e-05 6.053290e-05 5.963840e-05 5.874782e-05
## [18,] 6.361529e-05 6.273057e-05 6.184903e-05 6.097092e-05 6.009646e-05
## [19,] 6.489808e-05 6.403047e-05 6.316577e-05 6.230424e-05 6.144609e-05
## [20,] 6.618057e-05 6.533027e-05 6.448261e-05 6.363785e-05 6.279621e-05
## [21,] 6.746227e-05 6.662946e-05 6.579903e-05 6.497123e-05 6.414628e-05
## [22,] 6.874264e-05 6.792752e-05 6.711451e-05 6.630385e-05 6.549578e-05
## [23,] 7.002116e-05 6.922391e-05 6.842850e-05 6.763517e-05 6.684415e-05
## [24,] 7.129730e-05 7.051811e-05 6.974047e-05 6.896464e-05 6.819085e-05
## [25,] 7.257053e-05 7.180956e-05 7.104988e-05 7.029172e-05 6.953534e-05
## [26,] 7.384030e-05 7.309773e-05 7.235616e-05 7.161585e-05 7.087703e-05
## [27,] 7.510607e-05 7.438206e-05 7.365878e-05 7.293647e-05 7.221538e-05
## [28,] 7.636728e-05 7.566200e-05 7.495716e-05 7.425302e-05 7.354981e-05
## [29,] 7.762340e-05 7.693700e-05 7.625075e-05 7.556492e-05 7.487975e-05
## [30,] 7.887388e-05 7.820650e-05 7.753900e-05 7.687163e-05 7.620464e-05
## [31,] 8.011816e-05 7.946995e-05 7.882133e-05 7.817256e-05 7.752390e-05
## [32,] 8.135571e-05 8.072680e-05 8.009720e-05 7.946717e-05 7.883695e-05
## [33,] 8.258597e-05 8.197649e-05 8.136604e-05 8.075488e-05 8.014325e-05
## [34,] 8.380842e-05 8.321850e-05 8.262732e-05 8.203514e-05 8.144221e-05
## [35,] 8.502252e-05 8.445226e-05 8.388047e-05 8.330739e-05 8.273328e-05
## [36,] 8.622774e-05 8.567726e-05 8.512496e-05 8.457109e-05 8.401590e-05
## [37,] 8.742357e-05 8.689297e-05 8.636027e-05 8.582570e-05 8.528954e-05
## [38,] 8.860949e-05 8.809887e-05 8.758585e-05 8.707069e-05 8.655365e-05
## [39,] 8.978501e-05 8.929445e-05 8.880120e-05 8.830554e-05 8.780770e-05
## [40,] 9.094963e-05 9.047921e-05 9.000582e-05 8.952972e-05 8.905117e-05
## [41,] 9.210289e-05 9.165268e-05 9.119921e-05 9.074275e-05 9.028355e-05
## [42,] 9.324430e-05 9.281437e-05 9.238089e-05 9.194414e-05 9.150436e-05
## [43,] 9.437343e-05 9.396383e-05 9.355039e-05 9.313340e-05 9.271309e-05
## [44,] 9.548984e-05 9.510061e-05 9.470727e-05 9.431008e-05 9.390930e-05
## [45,] 9.659310e-05 9.622429e-05 9.585108e-05 9.547374e-05 9.509252e-05
## [46,] 9.768282e-05 9.733445e-05 9.698140e-05 9.662394e-05 9.626233e-05
## [47,] 9.875859e-05 9.843069e-05 9.809783e-05 9.776027e-05 9.741829e-05
## [48,] 9.982006e-05 9.951264e-05 9.919998e-05 9.888235e-05 9.856000e-05
## [49,] 1.008669e-04 1.005799e-04 1.002875e-04 9.998979e-05 9.968709e-05
## [50,] 1.018987e-04 1.016322e-04 1.013600e-04 1.010822e-04 1.007992e-04
## [51,] 1.029152e-04 1.026692e-04 1.024172e-04 1.021593e-04 1.018959e-04
## [52,] 1.039161e-04 1.036906e-04 1.034587e-04 1.032208e-04 1.029770e-04
## [53,] 1.049011e-04 1.046960e-04 1.044844e-04 1.042663e-04 1.040422e-04
## [54,] 1.058700e-04 1.056853e-04 1.054938e-04 1.052956e-04 1.050910e-04
## [55,] 1.068225e-04 1.066582e-04 1.064868e-04 1.063084e-04 1.061234e-04
## [56,] 1.077585e-04 1.076145e-04 1.074631e-04 1.073045e-04 1.071390e-04
## [57,] 1.086777e-04 1.085540e-04 1.084225e-04 1.082837e-04 1.081376e-04
## [58,] 1.095799e-04 1.094764e-04 1.093649e-04 1.092457e-04 1.091191e-04
## [59,] 1.104651e-04 1.103817e-04 1.102900e-04 1.101904e-04 1.100831e-04
## [60,] 1.113330e-04 1.112697e-04 1.111978e-04 1.111177e-04 1.110297e-04
## [61,] 1.121836e-04 1.121402e-04 1.120881e-04 1.120275e-04 1.119586e-04
## [62,] 1.130168e-04 1.129933e-04 1.129608e-04 1.129195e-04 1.128697e-04
## [63,] 1.138325e-04 1.138288e-04 1.138158e-04 1.137938e-04 1.137630e-04
## [64,] 1.146307e-04 1.146466e-04 1.146530e-04 1.146502e-04 1.146384e-04
## [65,] 1.154113e-04 1.154468e-04 1.154725e-04 1.154887e-04 1.154957e-04
## [66,] 1.161743e-04 1.162293e-04 1.162742e-04 1.163094e-04 1.163351e-04
## [67,] 1.169198e-04 1.169940e-04 1.170580e-04 1.171121e-04 1.171564e-04
## [68,] 1.176477e-04 1.177411e-04 1.178241e-04 1.178968e-04 1.179596e-04
## [69,] 1.183581e-04 1.184706e-04 1.185724e-04 1.186637e-04 1.187449e-04
## [70,] 1.190510e-04 1.191825e-04 1.193030e-04 1.194128e-04 1.195121e-04
## [71,] 1.197266e-04 1.198769e-04 1.200159e-04 1.201440e-04 1.202615e-04
## [72,] 1.203849e-04 1.205538e-04 1.207113e-04 1.208576e-04 1.209930e-04
## [73,] 1.210260e-04 1.212134e-04 1.213892e-04 1.215535e-04 1.217068e-04
## [74,] 1.216501e-04 1.218558e-04 1.220497e-04 1.222320e-04 1.224029e-04
## [75,] 1.222572e-04 1.224812e-04 1.226930e-04 1.228930e-04 1.230814e-04
## [76,] 1.228476e-04 1.230896e-04 1.233192e-04 1.235368e-04 1.237426e-04
## [77,] 1.234213e-04 1.236812e-04 1.239285e-04 1.241635e-04 1.243865e-04
## [78,] 1.239786e-04 1.242561e-04 1.245209e-04 1.247732e-04 1.250133e-04
## [79,] 1.245196e-04 1.248147e-04 1.250968e-04 1.253662e-04 1.256232e-04
## [80,] 1.250445e-04 1.253570e-04 1.256562e-04 1.259426e-04 1.262163e-04
## [81,] 1.255536e-04 1.258832e-04 1.261994e-04 1.265026e-04 1.267929e-04
## [82,] 1.260469e-04 1.263936e-04 1.267266e-04 1.270464e-04 1.273530e-04
## [83,] 1.265248e-04 1.268883e-04 1.272380e-04 1.275741e-04 1.278971e-04
## [84,] 1.269875e-04 1.273676e-04 1.277337e-04 1.280862e-04 1.284251e-04
## [85,] 1.274351e-04 1.278317e-04 1.282141e-04 1.285826e-04 1.289375e-04
## [86,] 1.278680e-04 1.282808e-04 1.286794e-04 1.290638e-04 1.294344e-04
## [87,] 1.282863e-04 1.287152e-04 1.291297e-04 1.295298e-04 1.299160e-04
## [88,] 1.286903e-04 1.291352e-04 1.295654e-04 1.299811e-04 1.303826e-04
## [89,] 1.290803e-04 1.295409e-04 1.299866e-04 1.304177e-04 1.308344e-04
## [90,] 1.294564e-04 1.299326e-04 1.303937e-04 1.308400e-04 1.312717e-04
## [91,] 1.298191e-04 1.303106e-04 1.307869e-04 1.312482e-04 1.316947e-04
## [92,] 1.301684e-04 1.306751e-04 1.311664e-04 1.316425e-04 1.321037e-04
## [93,] 1.305047e-04 1.310264e-04 1.315325e-04 1.320233e-04 1.324990e-04
## [94,] 1.308283e-04 1.313648e-04 1.318855e-04 1.323908e-04 1.328807e-04
## [95,] 1.311394e-04 1.316905e-04 1.322257e-04 1.327452e-04 1.332493e-04
## [96,] 1.314382e-04 1.320037e-04 1.325532e-04 1.330868e-04 1.336049e-04
## [97,] 1.317250e-04 1.323048e-04 1.328684e-04 1.334159e-04 1.339477e-04
## [98,] 1.320002e-04 1.325940e-04 1.331715e-04 1.337328e-04 1.342781e-04
## [99,] 1.322638e-04 1.328716e-04 1.334627e-04 1.340376e-04 1.345964e-04
## [100,] 1.325163e-04 1.331377e-04 1.337424e-04 1.343307e-04 1.349027e-04
## [,91] [,92] [,93] [,94] [,95]
## [1,] 3.656684e-05 3.546237e-05 3.436624e-05 3.327860e-05 3.219960e-05
## [2,] 3.785200e-05 3.675989e-05 3.567590e-05 3.460018e-05 3.353289e-05
## [3,] 3.914489e-05 3.806534e-05 3.699369e-05 3.593010e-05 3.487472e-05
## [4,] 4.044520e-05 3.937842e-05 3.831932e-05 3.726806e-05 3.622478e-05
## [5,] 4.175262e-05 4.069882e-05 3.965247e-05 3.861373e-05 3.758275e-05
## [6,] 4.306682e-05 4.202621e-05 4.099281e-05 3.996680e-05 3.894832e-05
## [7,] 4.438746e-05 4.336023e-05 4.234000e-05 4.132691e-05 4.032114e-05
## [8,] 4.571417e-05 4.470054e-05 4.369367e-05 4.269372e-05 4.170084e-05
## [9,] 4.704658e-05 4.604676e-05 4.505345e-05 4.406683e-05 4.308706e-05
## [10,] 4.838431e-05 4.739849e-05 4.641895e-05 4.544586e-05 4.447939e-05
## [11,] 4.972694e-05 4.875533e-05 4.778977e-05 4.683041e-05 4.587743e-05
## [12,] 5.107406e-05 5.011687e-05 4.916548e-05 4.822005e-05 4.728076e-05
## [13,] 5.242523e-05 5.148266e-05 5.054564e-05 4.961435e-05 4.868894e-05
## [14,] 5.378002e-05 5.285227e-05 5.192982e-05 5.101284e-05 5.010152e-05
## [15,] 5.513795e-05 5.422522e-05 5.331754e-05 5.241508e-05 5.151803e-05
## [16,] 5.649856e-05 5.560105e-05 5.470833e-05 5.382059e-05 5.293800e-05
## [17,] 5.786137e-05 5.697926e-05 5.610170e-05 5.522886e-05 5.436092e-05
## [18,] 5.922587e-05 5.835937e-05 5.749714e-05 5.663939e-05 5.578629e-05
## [19,] 6.059156e-05 5.974085e-05 5.889416e-05 5.805168e-05 5.721360e-05
## [20,] 6.195792e-05 6.112318e-05 6.029221e-05 5.946519e-05 5.864231e-05
## [21,] 6.332441e-05 6.250584e-05 6.169077e-05 6.087938e-05 6.007188e-05
## [22,] 6.469051e-05 6.388828e-05 6.308928e-05 6.229372e-05 6.150177e-05
## [23,] 6.605567e-05 6.526996e-05 6.448721e-05 6.370763e-05 6.293140e-05
## [24,] 6.741934e-05 6.665031e-05 6.588398e-05 6.512056e-05 6.436022e-05
## [25,] 6.878095e-05 6.802878e-05 6.727904e-05 6.653193e-05 6.578765e-05
## [26,] 7.013994e-05 6.940479e-05 6.867180e-05 6.794117e-05 6.721311e-05
## [27,] 7.149574e-05 7.077777e-05 7.006168e-05 6.934769e-05 6.863600e-05
## [28,] 7.284778e-05 7.214714e-05 7.144812e-05 7.075091e-05 7.005573e-05
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## [100,] 1.380090e-04 1.384749e-04 1.389267e-04 1.393647e-04 1.397891e-04
##
## $axis
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## [6] -6.14141414 -5.96969697 -5.79797980 -5.62626263 -5.45454545
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## [31] -1.84848485 -1.67676768 -1.50505051 -1.33333333 -1.16161616
## [36] -0.98989899 -0.81818182 -0.64646465 -0.47474747 -0.30303030
## [41] -0.13131313 0.04040404 0.21212121 0.38383838 0.55555556
## [46] 0.72727273 0.89898990 1.07070707 1.24242424 1.41414141
## [51] 1.58585859 1.75757576 1.92929293 2.10101010 2.27272727
## [56] 2.44444444 2.61616162 2.78787879 2.95959596 3.13131313
## [61] 3.30303030 3.47474747 3.64646465 3.81818182 3.98989899
## [66] 4.16161616 4.33333333 4.50505051 4.67676768 4.84848485
## [71] 5.02020202 5.19191919 5.36363636 5.53535354 5.70707071
## [76] 5.87878788 6.05050505 6.22222222 6.39393939 6.56565657
## [81] 6.73737374 6.90909091 7.08080808 7.25252525 7.42424242
## [86] 7.59595960 7.76767677 7.93939394 8.11111111 8.28282828
## [91] 8.45454545 8.62626263 8.79797980 8.96969697 9.14141414
## [96] 9.31313131 9.48484848 9.65656566 9.82828283 10.00000000dcc forecast
dccforecast = dccforecast(dccfit, n.head = 252)
dccforecast##
## *---------------------------------*
## * DCC GARCH Forecast *
## *---------------------------------*
##
## Distribution : mvnorm
## Model : DCC(1,1)
## Horizon : 1
## Roll Steps : 0
## -----------------------------------
##
## 0-roll forecast:
## , , 1
##
## [,1] [,2] [,3] [,4]
## [1,] 1.0000 0.4795 0.3984 0.4311
## [2,] 0.4795 1.0000 0.5485 0.6254
## [3,] 0.3984 0.5485 1.0000 0.6178
## [4,] 0.4311 0.6254 0.6178 1.0000