Assignment No 6

Stationary Time Series

Q. Use NSE Nifty Index (Feb 6, 2012 to Feb 6, 2013)
a. Create log of the return data.

b. Calculate Historical volatility.

c. Analyse Stationarity by-

    1. Create Auto Correlation Function Plot.

    2. Augmented Dickey Fuller Test.

Solution:

> nse1yr<-read.csv(file.choose(),header=T)

> closingprice<-nse1yr$Close

> closingprice.ts<-ts(closingprice,frequency=252)

> laggingtable<-cbind(closingprice.ts,lag(closingprice.ts,k=-1)

+ ,closingprice.ts-lag(closingprice.ts,k=-1))

> Return<-(closingprice.ts-lag(closingprice.ts,k=-1))/lag(closingprice.ts,k=-1)

> head(Return)

[1] -0.004942508  0.006185393  0.008233749 -0.005681451  0.001598038

[6]  0.004795740

> Return.Std<-scale(Return)+10

> logreturn<-log(Return.Std)

> acf(logreturn)

From the figure it implies that the all the standard errors are within the 95% confidence interval and hence we can say that the time series is stationary.

> T<-252^.5

> Historicalvolatility<-sd(Return)*T

> Historicalvolatility

[1] 0.1424954

> adf.test(logreturn)

        Augmented Dickey-Fuller Test

data:  logreturn

Dickey-Fuller = -6.2635, Lag order = 6, p-value = 0.01

alternative hypothesis: stationary

Warning message:

In adf.test(logreturn) : p-value smaller than printed p-value

 

Since p-value is less than 0.05 ,therefore we can say null hypothesis is rejected and unit root is not 1 hence the time series is stationary so data analysis can be done.