Investigating the Effect of Different Input Sample Size with Nested Conditional Mean and Variance Models over Market Returns Forecast in Volatile Market Conditions of 2008

In highly volatile market conditions it's always difficult to predict returns using heteroscedastic Garch models. This paper tries to investigate the impact of sample data inputs over forecast using nested conditional mean ARMAX(2, 2, 0) and conditional variance Garch(1, 1), Gjr-garch(1, 1) and Egarch(1, 1) models. Research also tries to indentify relationship between outcome of formal hypothesis tests, the Ljung-Box-Pierce Q-test and Engle's ARCH test, sample input and forecast results. Study is conducted over two diversified stock markets index of America (NASDAQ Composite) and Asia (Nikkei 225). Returns are forecasted for the volatile month of aug-08 using sample inputs of last one month, two months up to seven months before aug-08 and a complete year before inputi.e from 1-aug-07 to 31-jul-08 of 246 trading days has also been taken. Graphical and correlative comparison of forecasted and observed returns is also done to identify any trend followed by Garch models in relation to size of sample inputs and forecast. Results show that forecast of mean of returns is far more accurate with Nikkei as compared to Nasdaq.