Business App IT Lab - Session 6

Assignment 1
Create log returns data and calculate historical volatility

Data Set: NSE Nifty Indices Data from 1st Jan 2012 to 31st Jan 2013
Working Column : Closing Price named Close
Formula Used: (logSt - logS(t-1))/logS(t-1)

Commands:
> stockprice <- read.csv(file.choose(),header=T)
> closingprice <- stockprice$Close
> closingprice.ts <- ts(closingprice , frequency=252)
> log.returns1 <- log(closingprice.ts , base=exp(1)) - log(lag(closingprice.ts,k=-1), base = exp(1))
> log.returns <- log.returns1/log(lag(closingprice.ts,k=-1), base = exp(1))
> log.returns
> T = (252)^0.5
> historical.volatility <- sd(log.returns) *T
> historical.volatility

Assignment 2:
 Create acf plot and interpret the result for log returns data and do ADF test and interpret it. 

Command:
> acf(log.returns)

Graph Interpretation: The two dotted lines represent the confidence interval of 95%. This is a visual tool to interpret the stationarity of time series. Autocorrelation calculates the correlation between different time steps/lags within the same variable. Since the correlation measurements lie within the confidence interval and there is apparent pattern in the correlation we can say that time series is stationary. 

Augmented Dickey-Fuller(ADF) Test

Command:
>adf.test(log.returns)

Interpretation: Since the p value obtained in ADF test is 0.01 which is less than alpha . The default value of alpha is 0.05. So we are going to reject the null hypothesis and accept the alternate hypothesis. Here the alternate hypothesis is that the time series is stationary. Hence by looking at p value we can say that time series is stationary.