SESSION 6 - Business Application Lab

Question :  
(a) Create and plot the log of returns data for a 13 month period and interpret the stationarity.
(b) Calculate historical volatility of the same returns.
(c) Carry out adf test for returns and interpret the results.


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

         Date    Open    High     Low   Close Shares.Traded Turnover..Rs..Cr.
1 01-Dec-2011 1937.80 1973.40 1930.25 1945.50      91246016            791.90
2 02-Dec-2011 1947.90 1981.05 1936.55 1977.85      90348679            781.31
3 05-Dec-2011 1975.55 1986.40 1968.60 1975.85      88981133            691.75
4 07-Dec-2011 1978.10 2001.85 1973.50 1978.45      99171329            872.43
5 08-Dec-2011 1976.25 1976.25 1928.65 1934.50     104371626            820.01
6 09-Dec-2011 1920.80 1932.10 1901.90 1919.00      90902176            659.08

> closeprice<-z$Close
> closeprice.ts<-ts(closeprice, frequency=252)
> returns<-(closeprice.ts-lag(closeprice.ts,k=-1))/lag(closeprice.ts,k=-1)
> manipulate<-scale(returns)+10
> logreturns<-log(manipulate)
> logreturns
> acf(logreturns)

We can see from the graph that almost all the errors lie between the two dotted lines i.e. between 95% confidence interval. Thus, we can conclude that the time interval is stationary.


> T=(252)^0.5
> historicalvolatility<-sd(logreturns)*T

Warning message:
sd(<matrix>) is deprecated.
 Use apply(*, 2, sd) instead.

> historicalvolatility
[1] 1.620009

> adf.test(logreturns)

        Augmented Dickey-Fuller Test

data:  logreturns 

Dickey-Fuller = -5.2022, Lag order = 6, p-value = 0.01

alternative hypothesis: stationary 

Warning message:

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

Since p value is less that 0.5, we cannot accept the null hypothesis and so can conclude with 95% confidence that the time series is stationary and further analysis can be done