time-series-garch.r

#Install the Ecdat package
install.packages("Ecdat")
#Loading the library and the Garch dataset
library(Ecdat)
mydata=Garch
#Look at the dataset
str(mydata)

#Correct the data types of date and day
#Correcting date fixes it to some arbitrary date such that the trend is same but the mapping is different
mydata$date=as.Date(mydata$date, origin = "01-02-1980")
mydata$day=as.factor(mydata$day)

#Install packages and load them
install.packages("tseries")
install.packages("urca")
install.packages("fUnitRoots")
install.packages("forecast")
install.packages("fGarch")
library(fGarch) # estimate GARCH and Forecast
library(tseries) #used for time series data
library(urca)  #Used for checking Unit root Cointegration
library(fUnitRoots) #Used for conducting unit root test
library(forecast) #Used for forecasting ARIMA model

#Converting Dollar - Deutsche mark exchange rate to time series
exchange_rate_dollar_deutsch_mark <- ts(mydata$dm, start=c(1980, 1), end=c(1987, 5), frequency=266)
#Plot the time series
plot.ts(exchange_rate_dollar_deutsch_mark,  main="exchange_rate_dollar_deutsch_mark")

#Calculate inflation as difference of log of exchange rate and then multiplied by 100
inflation_series<-(diff(log(exchange_rate_dollar_deutsch_mark)))*100
#Plot the inflation
plot.ts(inflation_series,  main="Inflation of exchange rate")

summary(inflation_series)

#ACF and PACF Plots
acf(inflation_series)
pacf(inflation_series)

#Model fitting. We have selected the ARIMA(5,0,0) model
Arima_5_0_0<- arima(inflation_series[1:499], order = c(5,0,0))
#Check out the residuals
residual <- Arima_5_0_0$resid
acf(residual)
pacf(residual)

#Perform the Ljung Box test
Box.test(residual,c(20),"Ljung-Box")

#Fitting GARCH over the first 500 data points
garch.fit <- garchFit(formula = ~arma(5,0)+garch(1,1), data = inflation_series[1:500])

#Plot the model
plot(garch.fit)