Principal Component Analysis in Modelling Stock Market Returns

In this study, an alternative method to compare the performance of several GARCH models in fitting the KLCI daily rate of return series before and after the Asian financial crisis in 1997 using Principal Component Analysis (PCA) is sought. Comparison is then made with the results obtained from a known method based on the ranks of the Log Likelihood (Log L), Schwarzs Bayesian Criterion (SBC) and the Akaike Information Criterion (AIC) values. It is found that the best and the worst fit models identified by both methods are exactly the same for the two periods but some degree of disagreement, however, existed between the intermediate models. We also find that the proposed method has a clear edge over its rival because PCA uses actual values of the three criteria and hence the inability to exactly specify the relative position of each of the competing models as faced by the ranking method may be avoided. Another plus point is this method also enables models to be classified into several distinct groups ordered in such a way that each group is made up of models with nearly the same level of fitting ability. The two extreme classes of models are identified to represent the best and the worst groups respectively.