Analysis of Ibm Stock Data
Econometric Methods II Project / Assignment – I DRISHAN SENGUPTA (MB-1122) PROBLEM
Take a time series data of reasonable length on any financial variable of your interest. Instead of real time series, you may as well consider a time series of artificially generated (i.e., simulated) data such that the DGP of the series incorporates, inter alia, volatility.
i. Plot the data and comment on its nature. Check also if the time series is stationary.
ii. Fit an appropriate conditional mean model to this data. Test if the residuals of the model thus obtained are white noise. Also find empirically whether the squared residuals are autocorrelated or not.
iii. Fit an appropriate volatility model simultaneously with a mean model. Thereafter, test if the standardized residuals as well as the squared standardized residuals are autocorrelated.
iv. Estimate the risk-return type of relationship in the framework of (G)ARCH -In- Mean model, and then comment on the nature of the relationship thus obtained.
SOLUTION
DATA DESCRIPTION :
Monthly returns for IBM stock from 1926 to 1997.
(‘m.ibm2697’ object of class ‘zooreg’, package {FinTS} in R)
Source : http://faculty.chicagogsb.edu/ruey.tsay/teaching/fts2
PART (i)
A time series is said to be strictly stationary if the joint distribution of X(t1),……,X(tk) is the same as the joint distribution of X(t1+α),……….,X(tk+α) for all t1,…., tk,α. This is a quite strong condition to hold in real circumstances. Rather we define a weaker restriction ,called weak stationary , if it’s mean is constant and auto covariance depends on lag; i.e. E(X(t)]=µ
Take a time series data of reasonable length on any financial variable of your interest. Instead of real time series, you may as well consider a time series of artificially generated (i.e., simulated) data such that the DGP of the series incorporates, inter alia, volatility.
i. Plot the data and comment on its nature. Check also if the time series is stationary.
ii. Fit an appropriate conditional mean model to this data. Test if the residuals of the model thus obtained are white noise. Also find empirically whether the squared residuals are autocorrelated or not.
iii. Fit an appropriate volatility model simultaneously with a mean model. Thereafter, test if the standardized residuals as well as the squared standardized residuals are autocorrelated.
iv. Estimate the risk-return type of relationship in the framework of (G)ARCH -In- Mean model, and then comment on the nature of the relationship thus obtained.
SOLUTION
DATA DESCRIPTION :
Monthly returns for IBM stock from 1926 to 1997.
(‘m.ibm2697’ object of class ‘zooreg’, package {FinTS} in R)
Source : http://faculty.chicagogsb.edu/ruey.tsay/teaching/fts2
PART (i)
A time series is said to be strictly stationary if the joint distribution of X(t1),……,X(tk) is the same as the joint distribution of X(t1+α),……….,X(tk+α) for all t1,…., tk,α. This is a quite strong condition to hold in real circumstances. Rather we define a weaker restriction ,called weak stationary , if it’s mean is constant and auto covariance depends on lag; i.e. E(X(t)]=µ