library(rugarch)
## Loading required package: parallel
##
## Attaching package: 'rugarch'
## The following object is masked from 'package:stats':
##
## sigma
library(tseries)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(ggplot2)
data = read.csv("AUS.csv")
inflation = ts(data$INFLATION, start = c(2005, 1), frequency = 12)
infl = diff(inflation); infl
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2005 -0.05 0.17 -1.66 0.31 -0.07 -0.33 -0.22 0.45 0.28 0.37 -0.33
## 2006 0.23 0.99 1.34 0.98 -0.57 1.74 2.49 -0.22 -1.20 -1.24 -2.05 -0.64
## 2007 0.33 -0.21 -0.13 -0.08 0.14 -0.60 -0.80 0.27 1.18 0.39 0.94 0.23
## 2008 -0.69 -0.60 -0.75 -0.13 0.78 0.41 -0.16 0.21 -0.77 -0.70 -0.08 0.49
## 2009 0.07 0.34 0.17 1.76 -0.69 -0.28 -0.09 -0.89 -0.14 0.59 0.35 -0.06
## 2010 0.21 0.40 0.53 -1.62 -0.64 -1.12 -0.86 0.09 -0.03 0.34 -0.78 -0.47
## 2011 0.05 0.89 1.18 0.77 1.65 2.31 2.17 0.84 2.55 1.08 1.62 0.62
## 2012 0.79 -0.81 -1.59 -0.65 -1.14 -1.05 -1.53 -0.90 -2.86 -2.65 -1.12 -0.91
## 2013 -0.67 -0.66 0.03 0.01 0.35 -0.08 0.39 -0.22 0.31 1.21 0.77 -0.63
## 2014 -0.32 1.62 0.12 0.62 1.08 0.16 1.01 2.81 2.18 0.09 -1.47 4.61
## 2015 1.71 -0.80 -0.01 -0.40 -1.21 0.75 0.74 -2.49 -4.22 -1.32 -1.18 -3.70
## 2016 0.38 -0.70 0.15 -0.23 0.18 -1.41
ts.plot(inflation, main = "monthly inflation rates(2005-2018)", ylab = "inflation rates", col = "blue" )
#define EGARCH (2,2) model specification
spec_garch = ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1, 2)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm")
summary(spec_garch)
## Length Class Mode
## 1 uGARCHspec S4
spec_egarch = ugarchspec(variance.model = list(model = "eGARCH", garchOrder = c(2,2)),
mean.model = list(armaOrder = c(0,0), Include.mean = F),
distribution.model = "norm"); spec_egarch
## Warning: unidentified option(s) in mean.model:
## Include.mean
##
## *---------------------------------*
## * GARCH Model Spec *
## *---------------------------------*
##
## Conditional Variance Dynamics
## ------------------------------------
## GARCH Model : eGARCH(2,2)
## Variance Targeting : FALSE
##
## Conditional Mean Dynamics
## ------------------------------------
## Mean Model : ARFIMA(0,0,0)
## Include Mean : TRUE
## GARCH-in-Mean : FALSE
##
## Conditional Distribution
## ------------------------------------
## Distribution : norm
## Includes Skew : FALSE
## Includes Shape : FALSE
## Includes Lambda : FALSE
summary(spec_egarch)
## Length Class Mode
## 1 uGARCHspec S4
# fit the models
spec_garchfit = ugarchfit(infl, spec = spec_garch); spec_garchfit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : sGARCH(1,2)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu -0.011241 0.081542 -0.13786 0.890353
## omega 0.330177 0.155076 2.12913 0.033244
## alpha1 0.703361 0.254981 2.75848 0.005807
## beta1 0.057643 0.182410 0.31601 0.751998
## beta2 0.143082 0.110543 1.29436 0.195540
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu -0.011241 0.109043 -0.10309 0.917892
## omega 0.330177 0.187008 1.76558 0.077466
## alpha1 0.703361 0.293031 2.40029 0.016382
## beta1 0.057643 0.249570 0.23097 0.817339
## beta2 0.143082 0.083041 1.72303 0.084883
##
## LogLikelihood : -200.8692
##
## Information Criteria
## ------------------------------------
##
## Akaike 3.0054
## Bayes 3.1120
## Shibata 3.0028
## Hannan-Quinn 3.0487
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 13.78 2.056e-04
## Lag[2*(p+q)+(p+q)-1][2] 15.62 6.287e-05
## Lag[4*(p+q)+(p+q)-1][5] 22.57 3.787e-06
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.1846 0.6674
## Lag[2*(p+q)+(p+q)-1][8] 6.6827 0.1746
## Lag[4*(p+q)+(p+q)-1][14] 11.8023 0.1001
## d.o.f=3
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[4] 5.893 0.500 2.000 0.01520
## ARCH Lag[6] 7.359 1.461 1.711 0.03291
## ARCH Lag[8] 8.440 2.368 1.583 0.04999
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.2003
## Individual Statistics:
## mu 0.07604
## omega 0.27726
## alpha1 0.34289
## beta1 0.08881
## beta2 0.28129
##
## 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 1.4916 0.1382
## Negative Sign Bias 0.6617 0.5093
## Positive Sign Bias 1.2255 0.2226
## Joint Effect 2.5521 0.4660
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 11.47 0.9071
## 2 30 17.38 0.9560
## 3 40 32.05 0.7771
## 4 50 40.74 0.7934
##
##
## Elapsed time : 0.07421398
plot(spec_garchfit, which = 9)
plot(spec_garchfit, which = 1)
spec_egarchfit = ugarchfit(infl, spec = spec_egarch); spec_egarchfit
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : eGARCH(2,2)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 0.005685 0.082650 0.068787 0.945159
## omega -0.005251 0.025098 -0.209205 0.834288
## alpha1 0.051240 0.225519 0.227210 0.820260
## alpha2 0.183285 0.163887 1.118357 0.263414
## beta1 0.788775 0.317339 2.485593 0.012934
## beta2 0.182140 0.327029 0.556953 0.577560
## gamma1 0.585607 0.261028 2.243466 0.024867
## gamma2 -0.407287 0.269173 -1.513102 0.130254
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 0.005685 0.10178 0.055856 0.955456
## omega -0.005251 0.03204 -0.163873 0.869831
## alpha1 0.051240 0.30340 0.168888 0.865885
## alpha2 0.183285 0.15934 1.150307 0.250018
## beta1 0.788775 0.29778 2.648834 0.008077
## beta2 0.182140 0.34257 0.531681 0.594947
## gamma1 0.585607 0.31498 1.859168 0.063003
## gamma2 -0.407287 0.31133 -1.308207 0.190803
##
## LogLikelihood : -196.8653
##
## Information Criteria
## ------------------------------------
##
## Akaike 2.9907
## Bayes 3.1612
## Shibata 2.9844
## Hannan-Quinn 3.0600
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 19.66 9.253e-06
## Lag[2*(p+q)+(p+q)-1][2] 23.30 6.068e-07
## Lag[4*(p+q)+(p+q)-1][5] 33.10 4.218e-09
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01087 0.9170
## Lag[2*(p+q)+(p+q)-1][11] 6.25757 0.4018
## Lag[4*(p+q)+(p+q)-1][19] 11.83415 0.2775
## d.o.f=4
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[5] 3.301 0.500 2.000 0.06924
## ARCH Lag[7] 4.234 1.473 1.746 0.17724
## ARCH Lag[9] 5.594 2.402 1.619 0.20895
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.3976
## Individual Statistics:
## mu 0.32248
## omega 0.30582
## alpha1 0.06601
## alpha2 0.06150
## beta1 0.17169
## beta2 0.19065
## gamma1 0.14688
## gamma2 0.28097
##
## 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 1.6892 0.09354 *
## Negative Sign Bias 1.4513 0.14907
## Positive Sign Bias 0.9934 0.32234
## Joint Effect 3.5047 0.32016
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 16.43 0.6284
## 2 30 28.77 0.4773
## 3 40 37.89 0.5204
## 4 50 34.90 0.9359
##
##
## Elapsed time : 0.2112951
plot(spec_egarchfit, which = 9)
plot(spec_egarchfit, which = 1)
f = ugarchforecast(spec_garchfit, n.ahead = 60, confint = 0.95)
plot(f, which = 1)
g = ugarchforecast(spec_egarchfit, n.ahead = 60, confint = 0.95)
plot(g, which = 1) # choose EGarch because it is the best
infocriteria(spec_garchfit)
##
## Akaike 3.005389
## Bayes 3.111958
## Shibata 3.002848
## Hannan-Quinn 3.048696
infocriteria(spec_egarchfit)
##
## Akaike 2.990735
## Bayes 3.161245
## Shibata 2.984404
## Hannan-Quinn 3.060026