Granger Result Season
2023-02-14
Granger Causality Test
##載入套件
library(lmtest)
library(dplyr)
library(ggplot2)
library(openxlsx)
library(vars)
library(tseries)
library(jtools)
library(forecast)
library(urca)##建立時間序列
season <- read.xlsx("E:/summer program/new data/byseason1.xlsx", sheet = '內插')
biomass.timeseries <- ts(season$aboveground距平, start = c(1997,1),frequency = 4)
leaf.timeseries <- ts(season$leaf距平, start = c(1997,1),frequency = 4)
cover.timeseries <- ts(season$cover距平, start = c(1997,1),frequency = 4)
relative.timeseries <- ts(season$relative距平, start = c(1997,1),frequency = 4)
oni.timeseries <- ts(season$ONI0, start = c(1997,1),frequency = 4)
pmm.timeseries <- ts(season$PMM0, start = c(1997,1),frequency = 4)
nino4.timeseries <- ts(season$NINO40, start = c(1997,1),frequency = 4)
cp.timeseries <- ts(season$CPENSO0, start = c(1997,1),frequency = 4)
temp.timeseries <- ts(season$TX距平0, start = c(1997,1),frequency = 4)
rain.timeseries <- ts(season$PP距平0, start = c(1997,1),frequency = 4)
salt.timeseries <- ts(season$Salt距平0, start = c(1997,1),frequency = 4)##檢測平穩性
ADF法
adf.test(na.omit(cover.timeseries))
adf.test(na.omit(leaf.timeseries))
adf.test(na.omit(relative.timeseries))
adf.test(na.omit(biomass.timeseries))
adf.test(na.omit(pmm.timeseries))
adf.test(na.omit(oni.timeseries))
adf.test(na.omit(nino4.timeseries))
adf.test(na.omit(cp.timeseries))
adf.test(na.omit(temp.timeseries))
adf.test(na.omit(rain.timeseries))
adf.test(na.omit(salt.timeseries))##
## Augmented Dickey-Fuller Test
##
## data: na.omit(cover.timeseries)
## Dickey-Fuller = -1.6921, Lag order = 4, p-value = 0.7022
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(leaf.timeseries)
## Dickey-Fuller = -2.7016, Lag order = 4, p-value = 0.2881
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(relative.timeseries)
## Dickey-Fuller = -1.9812, Lag order = 4, p-value = 0.5836
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(biomass.timeseries)
## Dickey-Fuller = -1.2938, Lag order = 4, p-value = 0.8655
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(pmm.timeseries)
## Dickey-Fuller = -2.5903, Lag order = 4, p-value = 0.3325
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(oni.timeseries)
## Dickey-Fuller = -3.6285, Lag order = 4, p-value = 0.03462
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(nino4.timeseries)
## Dickey-Fuller = -3.4569, Lag order = 4, p-value = 0.04983
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(cp.timeseries)
## Dickey-Fuller = -3.834, Lag order = 4, p-value = 0.02091
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(temp.timeseries)
## Dickey-Fuller = -2.2262, Lag order = 4, p-value = 0.483
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(rain.timeseries)
## Dickey-Fuller = -4.7815, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary
##
##
## Augmented Dickey-Fuller Test
##
## data: na.omit(salt.timeseries)
## Dickey-Fuller = -2.4348, Lag order = 4, p-value = 0.3975
## alternative hypothesis: stationaryKPSS法
kpss.test(na.omit(cover.timeseries))
kpss.test(na.omit(leaf.timeseries))
kpss.test(na.omit(relative.timeseries))
kpss.test(na.omit(biomass.timeseries))
kpss.test(na.omit(pmm.timeseries))
kpss.test(na.omit(oni.timeseries))
kpss.test(na.omit(nino4.timeseries))
kpss.test(na.omit(cp.timeseries))
kpss.test(na.omit(temp.timeseries))
kpss.test(na.omit(rain.timeseries))
kpss.test(na.omit(salt.timeseries))##
## KPSS Test for Level Stationarity
##
## data: na.omit(cover.timeseries)
## KPSS Level = 0.8314, Truncation lag parameter = 3, p-value = 0.01
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(leaf.timeseries)
## KPSS Level = 0.15951, Truncation lag parameter = 3, p-value = 0.1
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(relative.timeseries)
## KPSS Level = 1.0795, Truncation lag parameter = 3, p-value = 0.01
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(biomass.timeseries)
## KPSS Level = 0.55658, Truncation lag parameter = 3, p-value = 0.02892
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(pmm.timeseries)
## KPSS Level = 0.8593, Truncation lag parameter = 3, p-value = 0.01
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(oni.timeseries)
## KPSS Level = 0.11392, Truncation lag parameter = 3, p-value = 0.1
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(nino4.timeseries)
## KPSS Level = 0.19939, Truncation lag parameter = 3, p-value = 0.1
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(cp.timeseries)
## KPSS Level = 0.22521, Truncation lag parameter = 3, p-value = 0.1
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(temp.timeseries)
## KPSS Level = 0.78001, Truncation lag parameter = 3, p-value = 0.01
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(rain.timeseries)
## KPSS Level = 0.12981, Truncation lag parameter = 3, p-value = 0.1
##
##
## KPSS Test for Level Stationarity
##
## data: na.omit(salt.timeseries)
## KPSS Level = 0.17933, Truncation lag parameter = 3, p-value = 0.1##檢測差分
ADF法
ndiffs(cover.timeseries, test="adf")
ndiffs(leaf.timeseries, test="adf")
ndiffs(relative.timeseries, test="adf")
ndiffs(biomass.timeseries, test="adf")
ndiffs(pmm.timeseries, test="adf")
ndiffs(oni.timeseries, test="adf")
ndiffs(nino4.timeseries, test="adf")
ndiffs(cp.timeseries, test="adf")
ndiffs(temp.timeseries, test="adf")
ndiffs(rain.timeseries, test="adf")
ndiffs(salt.timeseries, test="adf")## [1] 1
## [1] 0
## [1] 0
## [1] 1
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0KPSS法
ndiffs(cover.timeseries, test="kpss")
ndiffs(leaf.timeseries, test="kpss")
ndiffs(relative.timeseries, test="kpss")
ndiffs(biomass.timeseries, test="kpss")
ndiffs(pmm.timeseries, test="kpss")
ndiffs(oni.timeseries, test="kpss")
ndiffs(nino4.timeseries, test="kpss")
ndiffs(cp.timeseries, test="kpss")
ndiffs(temp.timeseries, test="kpss")
ndiffs(rain.timeseries, test="kpss")
ndiffs(salt.timeseries, test="kpss")## [1] 1
## [1] 0
## [1] 1
## [1] 1
## [1] 1
## [1] 0
## [1] 0
## [1] 0
## [1] 1
## [1] 0
## [1] 0cover, biomass必做差分；relative, PMM, temp可做可不做
##檢測季節性差分
nsdiffs(cover.timeseries)
nsdiffs(leaf.timeseries)
nsdiffs(relative.timeseries)
nsdiffs(biomass.timeseries)
nsdiffs(pmm.timeseries)
nsdiffs(oni.timeseries)
nsdiffs(nino4.timeseries)
nsdiffs(cp.timeseries)
nsdiffs(temp.timeseries)
nsdiffs(rain.timeseries)
nsdiffs(salt.timeseries)## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0
## [1] 0##差分比較
coverdiff <- diff(cover.timeseries)
par(mfrow=c(2,2))
plot.ts(cover.timeseries,main="原始cover")
plot.ts(coverdiff,main="一階差分cover")
acf(cover.timeseries, na = na.omit, ,main="原始cover"); acf(coverdiff, na = na.omit, main="一階差分cover")
biomassdiff <- diff(biomass.timeseries)
par(mfrow=c(2,2))
plot.ts(biomass.timeseries,main="原始biomass")
plot.ts(biomassdiff,main="一階差分biomass")
acf(biomass.timeseries, na = na.omit, ,main="原始biomass");acf(biomassdiff, na = na.omit, main="一階差分biomass")
relativediff <- diff(relative.timeseries)
#par(mfrow=c(2,2))
#plot.ts(relative.timeseries,main="原始relative")
#plot.ts(relativediff,main="一階差分relative")
#acf(relative.timeseries, na = na.omit, ,main="原始relative"); acf(relativediff, na = na.omit, main="一階差分relative")pmmdiff <- diff(pmm.timeseries)
#par(mfrow=c(2,2))
#plot.ts(pmm.timeseries,main="原始pmm")
#plot.ts(pmmdiff,main="一階差分pmm")
#acf(pmm.timeseries, na = na.omit, ,main="原始pmm");acf(pmmdiff, na = na.omit, main="一階差分pmm")tempdiff <- diff(temp.timeseries)
#par(mfrow=c(2,2))
#plot.ts(temp.timeseries,main="原始temp")
#plot.ts(tempdiff,main="一階差分temp")
#(temp.timeseries, na = na.omit, ,main="原始temp");acf(tempdiff, na = na.omit, main="一階差分temp")
##建立校準時間序列
因為差分的原理為第一項與第二項之差為新序列之第一項，因此計算a與b之格蘭傑因果時，其結果會與現實差了一個時間單位。然而當此差距會包含0時，將導致一盲區無法被計算(沒有自回歸)，因此需要建立一個向後推移一單位之時間序列。
biomass1.timeseries <- ts(season$aboveground距平1, start = c(1997,1),frequency = 4)
cover1.timeseries <- ts(season$cover距平1, start = c(1997,1),frequency = 4)
relative1.timeseries <- ts(season$relative距平1, start = c(1997,1),frequency = 4)
pmm1.timeseries <- ts(season$PMM1, start = c(1997,1),frequency = 4)
temp1.timeseries <- ts(season$TX距平1, start = c(1997,1),frequency = 4)##建立校準差分序列
cover1diff <- diff(cover1.timeseries)
relative1diff <- diff(relative1.timeseries)
biomass1diff <- diff(biomass1.timeseries)
pmm1diff <- diff(pmm1.timeseries)
temp1diff <- diff(temp1.timeseries)##檢測協整
cointegrating <- dplyr::select(season, PMM0, aboveground距平)
jotest=ca.jo(cointegrating, type="trace", K=2, ecdet="none", spec="longrun")
summary(jotest)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , with linear trend
##
## Eigenvalues (lambda):
## [1] 0.27585855 0.07132986
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 1 | 6.07 6.50 8.18 11.65
## r = 0 | 32.54 15.66 17.95 23.52
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## PMM0.l2 aboveground距平.l2
## PMM0.l2 1.000000 1.0000
## aboveground距平.l2 4.119389 252.7904
##
## Weights W:
## (This is the loading matrix)
##
## PMM0.l2 aboveground距平.l2
## PMM0.d -0.43640045 0.0030503342
## aboveground距平.d -0.01750535 -0.0007918103cointegrating <- dplyr::select(season, PMM0, relative距平)
jotest=ca.jo(cointegrating, type="trace", K=2, ecdet="none", spec="longrun")
summary(jotest)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , with linear trend
##
## Eigenvalues (lambda):
## [1] 0.2752749 0.1146393
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 1 | 9.98 6.50 8.18 11.65
## r = 0 | 36.39 15.66 17.95 23.52
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## PMM0.l2 relative距平.l2
## PMM0.l2 1.000000 1.000000
## relative距平.l2 -0.176644 1.115258
##
## Weights W:
## (This is the loading matrix)
##
## PMM0.l2 relative距平.l2
## PMM0.d -0.4081559 -0.02799225
## relative距平.d 0.7120284 -0.21818982
##Biomass與PMM的滯後選擇 & Granger Causality Test
BIOMASS差分與PMM
bio_pmm <- cbind(pmm.timeseries, biomassdiff)
VARselect(y=na.omit(bio_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 1 1 5
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -1.0142979 -1.0510566 -1.0587417 -1.0573471 -1.0670205 -0.9913257
## HQ(n) -0.9402701 -0.9276770 -0.8860102 -0.8352637 -0.7955852 -0.6705385
## SC(n) -0.8288989 -0.7420582 -0.6261439 -0.5011500 -0.3872240 -0.1879298
## FPE(n) 0.3626879 0.3497067 0.3472703 0.3481844 0.3455014 0.3737179
## 7 8
## AIC(n) -0.90715411 -0.8607084
## HQ(n) -0.53701509 -0.4412175
## SC(n) 0.01984113 0.1898862
## FPE(n) 0.40810781 0.4296932AIC best at 5, BIC(SC) best at 1.
grangertest(biomassdiff ~ pmm.timeseries, order = 1, data = bio_pmm)
grangertest(pmm.timeseries ~ biomassdiff, order = 1, data = bio_pmm)
grangertest(biomassdiff ~ pmm.timeseries, order = 5, data = bio_pmm)
grangertest(pmm.timeseries ~ biomassdiff, order = 5, data = bio_pmm)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:1) + Lags(pmm.timeseries, 1:1)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0.164 0.6866
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:1) + Lags(biomassdiff, 1:1)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 3.8065 0.0546 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:5) + Lags(pmm.timeseries, 1:5)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 0.7377 0.5978
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:5) + Lags(biomassdiff, 1:5)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 2.1196 0.0737 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Biomass lead PMM by 1 and 5. (實質上Biomass與PMM同時/領先4季)
BIOMASS1差分與PMM
bio1_pmm <- cbind(pmm.timeseries, biomass1diff)
VARselect(y=na.omit(bio1_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 2 1 3
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -0.9235428 -1.0423719 -1.0881076 -1.0168086 -0.9951740 -0.9836241
## HQ(n) -0.8495150 -0.9189922 -0.9153761 -0.7947252 -0.7237388 -0.6628370
## SC(n) -0.7381438 -0.7333735 -0.6555098 -0.4606114 -0.3153775 -0.1802282
## FPE(n) 0.3971436 0.3527570 0.3372206 0.3625893 0.3712379 0.3766072
## 7 8
## AIC(n) -0.90363397 -0.8821845
## HQ(n) -0.53349495 -0.4626936
## SC(n) 0.02336128 0.1684101
## FPE(n) 0.40954694 0.4205634AIC best at 3, BIC(SC) best at 1.
grangertest(biomass1diff ~ pmm.timeseries, order = 1, data = bio1_pmm)
grangertest(pmm.timeseries ~ biomass1diff, order = 1, data = bio1_pmm)
grangertest(biomass1diff ~ pmm.timeseries, order = 3, data = bio1_pmm)
grangertest(pmm.timeseries ~ biomass1diff, order = 3, data = bio1_pmm)## Granger causality test
##
## Model 1: biomass1diff ~ Lags(biomass1diff, 1:1) + Lags(pmm.timeseries, 1:1)
## Model 2: biomass1diff ~ Lags(biomass1diff, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0 0.9959
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:1) + Lags(biomass1diff, 1:1)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 2.3891 0.1262
## Granger causality test
##
## Model 1: biomass1diff ~ Lags(biomass1diff, 1:3) + Lags(pmm.timeseries, 1:3)
## Model 2: biomass1diff ~ Lags(biomass1diff, 1:3)
## Res.Df Df F Pr(>F)
## 1 73
## 2 76 -3 0.8312 0.481
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:3) + Lags(biomass1diff, 1:3)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 73
## 2 76 -3 3.2092 0.02793 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Biomass lead PMM by 3. (實質上Biomass領先PMM2季)
##BIOMASS差分與PMM差分
bio_pmmdiff <- cbind(pmmdiff, biomassdiff)
VARselect(y=na.omit(bio_pmmdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 2 2
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -0.8650512 -1.0477954 -0.9991713 -0.9772263 -0.9519731 -0.8752591
## HQ(n) -0.7910234 -0.9244157 -0.8264398 -0.7551429 -0.6805378 -0.5544719
## SC(n) -0.6796522 -0.7387969 -0.5665735 -0.4210292 -0.2721765 -0.0718632
## FPE(n) 0.4210659 0.3508490 0.3685859 0.3772292 0.3876272 0.4197116
## 7 8
## AIC(n) -0.7878636 -0.8624107
## HQ(n) -0.4177246 -0.4429198
## SC(n) 0.1391317 0.1881839
## FPE(n) 0.4598139 0.4289623AIC, BIC(SC) best at 2.
grangertest(biomassdiff ~ pmmdiff, order = 2, data = bio_pmmdiff)
grangertest(pmmdiff ~ biomassdiff, order = 2, data = bio_pmmdiff)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:2) + Lags(pmmdiff, 1:2)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.056 0.9455
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:2) + Lags(biomassdiff, 1:2)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.9167 0.4042No significant result.
##Biomass與CPENSO的滯後選擇 & Granger
BIOMASS差分與CPENSO
bio_cp <- cbind(cp.timeseries, biomassdiff)
VARselect(y=na.omit(bio_cp), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 2 2 3
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -3.32683904 -3.47991151 -3.5065544 -3.47740155 -3.4540930 -3.42831736
## HQ(n) -3.25131008 -3.35402991 -3.3303201 -3.25081466 -3.1771534 -3.10102520
## SC(n) -3.13711686 -3.16370788 -3.0638693 -2.90823502 -2.7584450 -2.60618793
## FPE(n) 0.03590989 0.03082394 0.0300371 0.03096887 0.0317688 0.03270223
## 7 8
## AIC(n) -3.33540562 -3.26958404
## HQ(n) -2.95776082 -2.84158660
## SC(n) -2.38679473 -2.19449171
## FPE(n) 0.03604363 0.03871911AIC best at 3, BIC(SC) best at 2.
grangertest(biomassdiff ~ cp.timeseries, order = 2, data = bio_cp)
grangertest(cp.timeseries ~ biomassdiff, order = 2, data = bio_cp)
grangertest(biomassdiff ~ cp.timeseries, order = 3, data = bio_cp)
grangertest(cp.timeseries ~ biomassdiff, order = 3, data = bio_cp)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:2) + Lags(cp.timeseries, 1:2)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 73
## 2 75 -2 0.2224 0.8011
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:2) + Lags(biomassdiff, 1:2)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:2)
## Res.Df Df F Pr(>F)
## 1 73
## 2 75 -2 0.4678 0.6282
## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:3) + Lags(cp.timeseries, 1:3)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:3)
## Res.Df Df F Pr(>F)
## 1 70
## 2 73 -3 1.1799 0.3237
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:3) + Lags(biomassdiff, 1:3)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 70
## 2 73 -3 1.5869 0.2003No significant result.
BIOMASS1差分與CPENSO
bio1_cp <- cbind(cp.timeseries, biomass1diff)
VARselect(y=na.omit(bio1_cp), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 2 2
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -3.35164045 -3.58520798 -3.51064014 -3.50825452 -3.4751757 -3.43204983
## HQ(n) -3.27661681 -3.46016858 -3.33558498 -3.28318359 -3.2000890 -3.10694738
## SC(n) -3.16338351 -3.27144642 -3.07137395 -2.94348370 -2.7849003 -2.61626975
## FPE(n) 0.03503009 0.02774282 0.02991312 0.03002476 0.0310999 0.03256969
## 7 8
## AIC(n) -3.37363716 -3.39545027
## HQ(n) -2.99851895 -2.97031630
## SC(n) -2.43235246 -2.32866094
## FPE(n) 0.03467392 0.03411421AIC, BIC(SC) best at 2.
grangertest(biomass1diff ~ cp.timeseries, order = 2, data = bio1_cp)
grangertest(cp.timeseries ~ biomass1diff, order = 2, data = bio1_cp)## Granger causality test
##
## Model 1: biomass1diff ~ Lags(biomass1diff, 1:2) + Lags(cp.timeseries, 1:2)
## Model 2: biomass1diff ~ Lags(biomass1diff, 1:2)
## Res.Df Df F Pr(>F)
## 1 74
## 2 76 -2 1.1817 0.3125
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:2) + Lags(biomass1diff, 1:2)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:2)
## Res.Df Df F Pr(>F)
## 1 74
## 2 76 -2 0.1179 0.889No significant result.
##Biomass與Temp的滯後選擇 & Granger
Biomass差分與Temp
temp_biomass <- cbind(temp.timeseries, biomassdiff)
VARselect(y=na.omit(temp_biomass), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 1 1 5
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -3.64030637 -3.66062270 -3.66806190 -3.67286969 -3.69050411 -3.65763917
## HQ(n) -3.56627857 -3.53724303 -3.49533036 -3.45078627 -3.41906882 -3.33685202
## SC(n) -3.45490732 -3.35162428 -3.23546412 -3.11667254 -3.01070759 -2.85424329
## FPE(n) 0.02624654 0.02572668 0.02555373 0.02546257 0.02506601 0.02597638
## 7 8
## AIC(n) -3.56761590 -3.49338562
## HQ(n) -3.19747688 -3.07389473
## SC(n) -2.64062066 -2.44279101
## FPE(n) 0.02853324 0.03088881AIC best at 5, BIC best at 1.
grangertest(biomassdiff ~ temp.timeseries, order = 1, data = temp_biomass)
grangertest(temp.timeseries ~ biomassdiff, order = 1, data = temp_biomass)
grangertest(biomassdiff ~ temp.timeseries, order = 5, data = temp_biomass)
grangertest(temp.timeseries ~ biomassdiff, order = 5, data = temp_biomass)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:1) + Lags(temp.timeseries, 1:1)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0.0149 0.9031
## Granger causality test
##
## Model 1: temp.timeseries ~ Lags(temp.timeseries, 1:1) + Lags(biomassdiff, 1:1)
## Model 2: temp.timeseries ~ Lags(temp.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0.112 0.7388
## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:5) + Lags(temp.timeseries, 1:5)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 0.2467 0.9401
## Granger causality test
##
## Model 1: temp.timeseries ~ Lags(temp.timeseries, 1:5) + Lags(biomassdiff, 1:5)
## Model 2: temp.timeseries ~ Lags(temp.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 1.6449 0.1602No significant result.
Biomass差分與Temp差分
tempdiff_biomassdiff <- cbind(tempdiff, biomassdiff)
VARselect(y=na.omit(tempdiff_biomassdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 2 2 4
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -3.49376123 -3.67425516 -3.60400469 -3.69556810 -3.69640297 -3.59724134
## HQ(n) -3.41973342 -3.55087548 -3.43127315 -3.47348469 -3.42496769 -3.27645419
## SC(n) -3.30836218 -3.36525674 -3.17140691 -3.13937096 -3.01660646 -2.79384546
## FPE(n) 0.03038896 0.02537834 0.02724419 0.02489112 0.02491859 0.02759364
## 7 8
## AIC(n) -3.51923404 -3.4295049
## HQ(n) -3.14909502 -3.0100140
## SC(n) -2.59223880 -2.3789103
## FPE(n) 0.02994767 0.0329264AIC best at 5, BIC(SC) best at 2.
grangertest(biomassdiff ~ tempdiff, order = 2, data = tempdiff_biomassdiff)
grangertest(tempdiff ~ biomassdiff, order = 2, data = tempdiff_biomassdiff)
grangertest(biomassdiff ~ tempdiff, order = 5, data = tempdiff_biomassdiff)
grangertest(tempdiff ~ biomassdiff, order = 5, data = tempdiff_biomassdiff)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:2) + Lags(tempdiff, 1:2)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.5751 0.5651
## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:2) + Lags(biomassdiff, 1:2)
## Model 2: tempdiff ~ Lags(tempdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.7493 0.4761
## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:5) + Lags(tempdiff, 1:5)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 0.2461 0.9403
## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:5) + Lags(biomassdiff, 1:5)
## Model 2: tempdiff ~ Lags(tempdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 67
## 2 72 -5 1.9062 0.1049No significant result.
##Relative與PMM的滯後選擇 & Granger
Relative與PMM
relative_pmm <- cbind(relative.timeseries, pmm.timeseries)
VARselect(y=na.omit(relative_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 4 1 5
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 5.868147 5.899378 5.803772 5.712034 5.706870 5.760257
## HQ(n) 5.941684 6.021940 5.975360 5.932646 5.976507 6.078919
## SC(n) 6.052152 6.206053 6.233118 6.264050 6.381556 6.557613
## FPE(n) 353.622024 364.949309 331.895280 303.161882 302.162347 319.593304
## 7 8
## AIC(n) 5.817841 5.810112
## HQ(n) 6.185528 6.226823
## SC(n) 6.737867 6.852808
## FPE(n) 339.793725 338.830099AIC best at 5, BIC(SC) best at 4.
grangertest(relative.timeseries ~ pmm.timeseries, order = 4, data = relative_pmm)
grangertest(pmm.timeseries ~ relative.timeseries, order = 4, data = relative_pmm)
grangertest(relative.timeseries ~ pmm.timeseries, order = 5, data = relative_pmm)
grangertest(pmm.timeseries ~ relative.timeseries, order = 5, data = relative_pmm)## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:4) + Lags(pmm.timeseries, 1:4)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:4)
## Res.Df Df F Pr(>F)
## 1 71
## 2 75 -4 1.7013 0.1593
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:4) + Lags(relative.timeseries, 1:4)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:4)
## Res.Df Df F Pr(>F)
## 1 71
## 2 75 -4 0.6781 0.6094
## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:5) + Lags(pmm.timeseries, 1:5)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 1.453 0.2168
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:5) + Lags(relative.timeseries, 1:5)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 0.6228 0.6828No significant result.
Relative差分與PMM
relativediff_pmm <- cbind(relativediff, pmm.timeseries)
VARselect(y=na.omit(relativediff_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 4 3 4
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 6.030442 5.910832 5.760681 5.696243 5.788842 5.852497
## HQ(n) 6.104470 6.034211 5.933412 5.918326 6.060277 6.173284
## SC(n) 6.215841 6.219830 6.193278 6.252440 6.468638 6.655893
## FPE(n) 415.934349 369.159127 317.910613 298.439383 328.029474 350.572911
## 7 8
## AIC(n) 5.862792 5.907197
## HQ(n) 6.232931 6.326688
## SC(n) 6.789787 6.957792
## FPE(n) 355.570045 373.613494AIC best at 4, BIC(SC) best at 3.
grangertest(relativediff ~ pmm.timeseries, order = 3, data = relativediff_pmm)
grangertest(pmm.timeseries ~ relativediff, order = 3, data = relativediff_pmm)
grangertest(relativediff ~ pmm.timeseries, order = 4, data = relativediff_pmm)
grangertest(pmm.timeseries ~ relativediff, order = 4, data = relativediff_pmm)## Granger causality test
##
## Model 1: relativediff ~ Lags(relativediff, 1:3) + Lags(pmm.timeseries, 1:3)
## Model 2: relativediff ~ Lags(relativediff, 1:3)
## Res.Df Df F Pr(>F)
## 1 73
## 2 76 -3 0.3755 0.7709
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:3) + Lags(relativediff, 1:3)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 73
## 2 76 -3 0.725 0.5403
## Granger causality test
##
## Model 1: relativediff ~ Lags(relativediff, 1:4) + Lags(pmm.timeseries, 1:4)
## Model 2: relativediff ~ Lags(relativediff, 1:4)
## Res.Df Df F Pr(>F)
## 1 70
## 2 74 -4 1.0708 0.3776
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:4) + Lags(relativediff, 1:4)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:4)
## Res.Df Df F Pr(>F)
## 1 70
## 2 74 -4 0.7628 0.553No significant result.
Relative與PMM差分
relative_pmmdiff <- cbind(relative.timeseries, pmmdiff)
VARselect(y=na.omit(relative_pmmdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 3 2 4
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 6.091553 5.947278 5.838513 5.828347 5.828824 5.895855
## HQ(n) 6.165090 6.069840 6.010101 6.048959 6.098461 6.214518
## SC(n) 6.275558 6.253953 6.267859 6.380363 6.503510 6.693212
## FPE(n) 442.143560 382.855881 343.628321 340.556212 341.353477 366.005437
## 7 8
## AIC(n) 5.956517 5.948695
## HQ(n) 6.324204 6.365407
## SC(n) 6.876543 6.991392
## FPE(n) 390.338449 389.195819AIC best at 4, BIC(SC) best at 5.
grangertest(relative.timeseries ~ pmmdiff, order = 4, data = relative_pmmdiff)
grangertest(pmmdiff ~ relative.timeseries, order = 4, data = relative_pmmdiff)
grangertest(relative.timeseries ~ pmmdiff, order = 5, data = relative_pmmdiff)
grangertest(pmmdiff ~ relative.timeseries, order = 5, data = relative_pmmdiff)## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:4) + Lags(pmmdiff, 1:4)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:4)
## Res.Df Df F Pr(>F)
## 1 71
## 2 75 -4 1.0267 0.3995
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:4) + Lags(relative.timeseries, 1:4)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:4)
## Res.Df Df F Pr(>F)
## 1 71
## 2 75 -4 0.6345 0.6395
## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:5) + Lags(pmmdiff, 1:5)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 0.7802 0.5675
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:5) + Lags(relative.timeseries, 1:5)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 0.6524 0.6606No significant result.
Relative差分與PMM差分
relativediff_pmmdiff <- cbind(relative.timeseries, pmmdiff)
VARselect(y=na.omit(relativediff_pmmdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 3 2 4
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 6.091553 5.947278 5.838513 5.828347 5.828824 5.895855
## HQ(n) 6.165090 6.069840 6.010101 6.048959 6.098461 6.214518
## SC(n) 6.275558 6.253953 6.267859 6.380363 6.503510 6.693212
## FPE(n) 442.143560 382.855881 343.628321 340.556212 341.353477 366.005437
## 7 8
## AIC(n) 5.956517 5.948695
## HQ(n) 6.324204 6.365407
## SC(n) 6.876543 6.991392
## FPE(n) 390.338449 389.195819AIC best at 5, BIC(SC) best at 2.
grangertest(relative.timeseries ~ pmmdiff, order = 2, data = relativediff_pmmdiff)
grangertest(pmmdiff ~ relative.timeseries, order = 2, data = relativediff_pmmdiff)
grangertest(relative.timeseries ~ pmmdiff, order = 5, data = relativediff_pmmdiff)
grangertest(pmmdiff ~ relative.timeseries, order = 5, data = relativediff_pmmdiff)## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:2) + Lags(pmmdiff, 1:2)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:2)
## Res.Df Df F Pr(>F)
## 1 77
## 2 79 -2 0.1033 0.9019
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:2) + Lags(relative.timeseries, 1:2)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 77
## 2 79 -2 1.215 0.3023
## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:5) + Lags(pmmdiff, 1:5)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 0.7802 0.5675
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:5) + Lags(relative.timeseries, 1:5)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:5)
## Res.Df Df F Pr(>F)
## 1 68
## 2 73 -5 0.6524 0.6606No significant result.
##Relative與CPENSO的滯後選擇 & Granger
Relative與CPENSO
relative_cp <- cbind(relative.timeseries, cp.timeseries)
VARselect(y=na.omit(relative_cp), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 3 1 5
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 3.463226 3.392821 3.338482 3.309696 3.284896 3.364201 3.458966
## HQ(n) 3.538250 3.517861 3.513537 3.534767 3.559983 3.689303 3.834084
## SC(n) 3.651483 3.706583 3.777748 3.874467 3.975172 4.179981 4.400251
## FPE(n) 31.922740 29.762549 28.209637 27.445923 26.830024 29.133169 32.163613
## 8
## AIC(n) 3.417735
## HQ(n) 3.842869
## SC(n) 4.484524
## FPE(n) 31.035873AIC best at 3, BIC(SC) best at 1.
grangertest(relative.timeseries ~ cp.timeseries, order = 1, data = relative_cp)
grangertest(cp.timeseries ~ relative.timeseries, order = 1, data = relative_cp)
grangertest(relative.timeseries ~ cp.timeseries, order = 3, data = relative_cp)
grangertest(cp.timeseries ~ relative.timeseries, order = 3, data = relative_cp)## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:1) + Lags(cp.timeseries, 1:1)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 77
## 2 78 -1 0.8173 0.3688
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:1) + Lags(relative.timeseries, 1:1)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 77
## 2 78 -1 0.4553 0.5019
## Granger causality test
##
## Model 1: relative.timeseries ~ Lags(relative.timeseries, 1:3) + Lags(cp.timeseries, 1:3)
## Model 2: relative.timeseries ~ Lags(relative.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 71
## 2 74 -3 0.4945 0.6872
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:3) + Lags(relative.timeseries, 1:3)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 71
## 2 74 -3 0.9064 0.4425No significant result.
Relative差分與CPENSO
relativediff_cp <- cbind(relativediff, cp.timeseries)
VARselect(y=na.omit(relative_cp), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 5 3 1 5
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 3.463226 3.392821 3.338482 3.309696 3.284896 3.364201 3.458966
## HQ(n) 3.538250 3.517861 3.513537 3.534767 3.559983 3.689303 3.834084
## SC(n) 3.651483 3.706583 3.777748 3.874467 3.975172 4.179981 4.400251
## FPE(n) 31.922740 29.762549 28.209637 27.445923 26.830024 29.133169 32.163613
## 8
## AIC(n) 3.417735
## HQ(n) 3.842869
## SC(n) 4.484524
## FPE(n) 31.035873AIC best at 3, BIC(SC) best at 1.
grangertest(relativediff ~ cp.timeseries, order = 1, data = relativediff_cp)
grangertest(cp.timeseries ~ relativediff, order = 1, data = relativediff_cp)
grangertest(relativediff ~ cp.timeseries, order = 3, data = relativediff_cp)
grangertest(cp.timeseries ~ relativediff, order = 3, data = relativediff_cp)## Granger causality test
##
## Model 1: relativediff ~ Lags(relativediff, 1:1) + Lags(cp.timeseries, 1:1)
## Model 2: relativediff ~ Lags(relativediff, 1:1)
## Res.Df Df F Pr(>F)
## 1 76
## 2 77 -1 0.0444 0.8338
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:1) + Lags(relativediff, 1:1)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 76
## 2 77 -1 0.3763 0.5414
## Granger causality test
##
## Model 1: relativediff ~ Lags(relativediff, 1:3) + Lags(cp.timeseries, 1:3)
## Model 2: relativediff ~ Lags(relativediff, 1:3)
## Res.Df Df F Pr(>F)
## 1 70
## 2 73 -3 0.2144 0.8861
## Granger causality test
##
## Model 1: cp.timeseries ~ Lags(cp.timeseries, 1:3) + Lags(relativediff, 1:3)
## Model 2: cp.timeseries ~ Lags(cp.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 70
## 2 73 -3 1.2304 0.3052No significant result.
##Temp與PMM的滯後選擇 & Granger
Temp與PMM
temp_pmm <- cbind(temp.timeseries, pmm.timeseries)
VARselect(y=na.omit(temp_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 3 3 3
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) 0.2589601 0.1756239 -0.01794214 0.03566198 0.06342978 0.1163690
## HQ(n) 0.3270095 0.2890395 0.14083963 0.23980997 0.31294398 0.4112494
## SC(n) 0.4278695 0.4571395 0.37617963 0.54238997 0.68276398 0.8483094
## FPE(n) 1.2956506 1.1922818 0.98287977 1.03779402 1.06828936 1.1283142
## 7 8
## AIC(n) 0.1906305 0.1807359
## HQ(n) 0.5308772 0.5663488
## SC(n) 1.0351772 1.1378888
## FPE(n) 1.2181721 1.2099386AIC, BIC(SC) best at 3.
grangertest(temp.timeseries ~ pmm.timeseries, order = 3, data = temp_pmm)
grangertest(pmm.timeseries ~ temp.timeseries, order = 3, data = temp_pmm)## Granger causality test
##
## Model 1: temp.timeseries ~ Lags(temp.timeseries, 1:3) + Lags(pmm.timeseries, 1:3)
## Model 2: temp.timeseries ~ Lags(temp.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 86
## 2 89 -3 3.098 0.03099 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:3) + Lags(temp.timeseries, 1:3)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 86
## 2 89 -3 3.9452 0.01093 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1PMM 領先 Temp 3季; Temp 領先 PMM 3季.
Temp差分與PMM
tempdiff_pmm <- cbind(tempdiff, pmm.timeseries)
VARselect(y=na.omit(tempdiff_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 3 3 4
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 0.5346566 0.3465812 0.1300685 0.08766693 0.1421680 0.2154293 0.2888470
## HQ(n) 0.6031355 0.4607128 0.2898527 0.29310386 0.3932576 0.5121715 0.6312419
## SC(n) 0.7047192 0.6300189 0.5268813 0.59785482 0.7657310 0.9523673 1.1391601
## FPE(n) 1.7069553 1.4145830 1.1397007 1.09324743 1.1559115 1.2459999 1.3442083
## 8
## AIC(n) 0.3104210
## HQ(n) 0.6984685
## SC(n) 1.2741092
## FPE(n) 1.3779586AIC best at 4, BIC(SC) best at 3.
grangertest(tempdiff ~ pmm.timeseries, order = 3, data = tempdiff_pmm)
grangertest(pmm.timeseries ~ tempdiff, order = 3, data = tempdiff_pmm)
grangertest(tempdiff ~ pmm.timeseries, order = 4, data = tempdiff_pmm)
grangertest(pmm.timeseries ~ tempdiff, order = 4, data = tempdiff_pmm)## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:3) + Lags(pmm.timeseries, 1:3)
## Model 2: tempdiff ~ Lags(tempdiff, 1:3)
## Res.Df Df F Pr(>F)
## 1 85
## 2 88 -3 2.7238 0.04927 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:3) + Lags(tempdiff, 1:3)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 85
## 2 88 -3 2.817 0.04392 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:4) + Lags(pmm.timeseries, 1:4)
## Model 2: tempdiff ~ Lags(tempdiff, 1:4)
## Res.Df Df F Pr(>F)
## 1 82
## 2 86 -4 1.0453 0.389
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:4) + Lags(tempdiff, 1:4)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:4)
## Res.Df Df F Pr(>F)
## 1 82
## 2 86 -4 2.3089 0.06478 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1PMM lead Temp by 3; Temp lead PMM by 3 and 4. (實質上PMM領先Temp 4季；Temp領先PMM 2和3季)
Temp與PMM差分
temp_pmmdiff <- cbind(temp.timeseries, pmmdiff)
VARselect(y=na.omit(temp_pmmdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 3 3 2 3
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 0.4747269 0.2168313 0.1543781 0.1744728 0.1818065 0.2263362 0.2233073
## HQ(n) 0.5432059 0.3309629 0.3141624 0.3799097 0.4328961 0.5230785 0.5657021
## SC(n) 0.6447896 0.5002690 0.5511909 0.6846607 0.8053695 0.9632743 1.0736204
## FPE(n) 1.6076631 1.2424496 1.1677459 1.1923885 1.2026503 1.2596643 1.2589342
## 8
## AIC(n) 0.2540264
## HQ(n) 0.6420739
## SC(n) 1.2177146
## FPE(n) 1.3023997AIC best at 3, BIC(SC) best at 2.
grangertest(temp.timeseries ~ pmmdiff, order = 2, data = temp_pmmdiff)
grangertest(pmmdiff ~ temp.timeseries, order = 2, data = temp_pmmdiff)
grangertest(temp.timeseries ~ pmmdiff, order = 3, data = temp_pmmdiff)
grangertest(pmmdiff ~ temp.timeseries, order = 3, data = temp_pmmdiff)## Granger causality test
##
## Model 1: temp.timeseries ~ Lags(temp.timeseries, 1:2) + Lags(pmmdiff, 1:2)
## Model 2: temp.timeseries ~ Lags(temp.timeseries, 1:2)
## Res.Df Df F Pr(>F)
## 1 88
## 2 90 -2 3.8896 0.02406 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:2) + Lags(temp.timeseries, 1:2)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 88
## 2 90 -2 0.1097 0.8962
## Granger causality test
##
## Model 1: temp.timeseries ~ Lags(temp.timeseries, 1:3) + Lags(pmmdiff, 1:3)
## Model 2: temp.timeseries ~ Lags(temp.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 85
## 2 88 -3 2.2637 0.08689 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:3) + Lags(temp.timeseries, 1:3)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:3)
## Res.Df Df F Pr(>F)
## 1 85
## 2 88 -3 1.6811 0.1772PMM lead Temp by 2 and 3. (實質上PMM領先Temp 3和4季)
Temp差分與PMM差分
tempdiff_pmmdiff <- cbind(tempdiff, pmmdiff)
VARselect(y=na.omit(tempdiff_pmmdiff), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 3 2 4
##
## $criteria
## 1 2 3 4 5 6 7
## AIC(n) 0.6492568 0.2127901 0.1605420 0.1354522 0.1936255 0.2625013 0.2667114
## HQ(n) 0.7177358 0.3269217 0.3203263 0.3408892 0.4447150 0.5592436 0.6091063
## SC(n) 0.8193194 0.4962278 0.5573548 0.6456401 0.8171884 0.9994394 1.1170246
## FPE(n) 1.9142225 1.2374387 1.1749660 1.1467569 1.2169486 1.3060540 1.3147804
## 8
## AIC(n) 0.3140577
## HQ(n) 0.7021052
## SC(n) 1.2777459
## FPE(n) 1.3829789AIC best at 4, BIC(SC) best at 2.
grangertest(tempdiff ~ pmmdiff, order = 2, data = tempdiff_pmmdiff)
grangertest(pmmdiff ~ tempdiff, order = 2, data = tempdiff_pmmdiff)
grangertest(tempdiff ~ pmmdiff, order = 4, data = tempdiff_pmmdiff)
grangertest(pmmdiff ~ tempdiff, order = 4, data = tempdiff_pmmdiff)## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:2) + Lags(pmmdiff, 1:2)
## Model 2: tempdiff ~ Lags(tempdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 88
## 2 90 -2 3.7053 0.02851 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:2) + Lags(tempdiff, 1:2)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 88
## 2 90 -2 2.0579 0.1338
## Granger causality test
##
## Model 1: tempdiff ~ Lags(tempdiff, 1:4) + Lags(pmmdiff, 1:4)
## Model 2: tempdiff ~ Lags(tempdiff, 1:4)
## Res.Df Df F Pr(>F)
## 1 82
## 2 86 -4 1.0528 0.3853
## Granger causality test
##
## Model 1: pmmdiff ~ Lags(pmmdiff, 1:4) + Lags(tempdiff, 1:4)
## Model 2: pmmdiff ~ Lags(pmmdiff, 1:4)
## Res.Df Df F Pr(>F)
## 1 82
## 2 86 -4 2.3456 0.06135 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1PMM 領先 Temp 2季; Temp 領先 PMM by 4季.
##Salt與PMM的滯後選擇 & Granger
Salt與PMM
salt_pmm <- cbind(salt.timeseries, pmm.timeseries)
VARselect(y=na.omit(salt_pmm), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 4 1 1 4
##
## $criteria
## 1 2 3 4 5 6 7 8
## AIC(n) 1.793458 1.775214 1.764027 1.733818 1.804333 1.883607 1.932778 1.961071
## HQ(n) 1.866995 1.897776 1.935615 1.954430 2.073970 2.202269 2.300465 2.377782
## SC(n) 1.977463 2.081889 2.193373 2.285834 2.479019 2.680963 2.852804 3.003767
## FPE(n) 6.010691 5.903791 5.842007 5.674889 6.100847 6.622013 6.981580 7.217133AIC best at 3, BIC(SC) best at 1.
grangertest(salt.timeseries ~ pmm.timeseries, order = 1, data = relative_pmm)
grangertest(pmm.timeseries ~ salt.timeseries, order = 1, data = relative_pmm)
grangertest(salt.timeseries ~ pmm.timeseries, order = 3, data = relative_pmm)
grangertest(pmm.timeseries ~ salt.timeseries, order = 3, data = relative_pmm)## Granger causality test
##
## Model 1: salt.timeseries ~ Lags(salt.timeseries, 1:1) + Lags(pmm.timeseries, 1:1)
## Model 2: salt.timeseries ~ Lags(salt.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 80
## 2 81 -1 8.6202 0.004339 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:1) + Lags(salt.timeseries, 1:1)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 80
## 2 81 -1 0.3919 0.5331
## Granger causality test
##
## Model 1: salt.timeseries ~ Lags(salt.timeseries, 1:3) + Lags(pmm.timeseries, 1:3)
## Model 2: salt.timeseries ~ Lags(salt.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 74
## 2 77 -3 2.0146 0.1192
## Granger causality test
##
## Model 1: pmm.timeseries ~ Lags(pmm.timeseries, 1:3) + Lags(salt.timeseries, 1:3)
## Model 2: pmm.timeseries ~ Lags(pmm.timeseries, 1:3)
## Res.Df Df F Pr(>F)
## 1 74
## 2 77 -3 0.4773 0.699PMM 領先 salt 1季.
Salt與PMM
salt_biomass <- cbind(salt.timeseries, biomassdiff)
VARselect(y=na.omit(salt_biomass), lag.max = 8, type = c("const"))## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 1 2
##
## $criteria
## 1 2 3 4 5 6
## AIC(n) -2.0013017 -2.1037585 -2.0286503 -2.0782186 -2.0553771 -2.0522108
## HQ(n) -1.9272739 -1.9803788 -1.8559188 -1.8561352 -1.7839418 -1.7314236
## SC(n) -1.8159026 -1.7947601 -1.5960526 -1.5220214 -1.3755806 -1.2488149
## FPE(n) 0.1351708 0.1220454 0.1316563 0.1254442 0.1285914 0.1293622
## 7 8
## AIC(n) -2.0603694 -2.0663946
## HQ(n) -1.6902304 -1.6469037
## SC(n) -1.1333742 -1.0158000
## FPE(n) 0.1288071 0.1286873AIC best at 2, BIC(SC) best at 1.
grangertest(biomassdiff ~ salt.timeseries, order = 1, data = salt_biomass)
grangertest(salt.timeseries ~ biomassdiff, order = 1, data = salt_biomass)
grangertest(biomassdiff ~ salt.timeseries, order = 2, data = salt_biomass)
grangertest(salt.timeseries ~ biomassdiff, order = 2, data = salt_biomass)## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:1) + Lags(salt.timeseries, 1:1)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0.9089 0.3433
## Granger causality test
##
## Model 1: salt.timeseries ~ Lags(salt.timeseries, 1:1) + Lags(biomassdiff, 1:1)
## Model 2: salt.timeseries ~ Lags(salt.timeseries, 1:1)
## Res.Df Df F Pr(>F)
## 1 79
## 2 80 -1 0.0019 0.9653
## Granger causality test
##
## Model 1: biomassdiff ~ Lags(biomassdiff, 1:2) + Lags(salt.timeseries, 1:2)
## Model 2: biomassdiff ~ Lags(biomassdiff, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.8818 0.4182
## Granger causality test
##
## Model 1: salt.timeseries ~ Lags(salt.timeseries, 1:2) + Lags(biomassdiff, 1:2)
## Model 2: salt.timeseries ~ Lags(salt.timeseries, 1:2)
## Res.Df Df F Pr(>F)
## 1 76
## 2 78 -2 0.931 0.3986No significant result.