Modified non-transformed principal component and adaptive penalized high dimension for grouping effect of stock market price

Abstract

Nonstationary time series is complex and difficult to be modelled. Many researchers resolved it by transforming it into stationary time series. However, loss of generality will occur which make its inference more difficult. To overcome this, therefore a modified non-transformed approach is proposed using generalized dynamic principal component on the nonstationary series. On the other hand, the selection of informative variables is more importance, especially when the number of explanatory variables is larger than the number of observations. This is pertinent in order to achieve a better model interpretation of the highly correlated variables. Thus, the penalized likelihood methods are mostly adapted since they are able to perform variable selection and model estimation concomitantly. Nevertheless, the scarceness in the consistency of variable selection, encouragement of grouping effects and robustness can be found in the majority of these methods. Therefore, to overcome these shortcomings, several improvements in the high dimensional penalized methods are proposed in this study. The performance of homogenous variable selection was improved using ordered homogeneity pursuit least absolute shrinkage and selection operator method. An initial weight which is distance correlation is proposed in the adaptive elastic net to encourage grouping effects between highly correlated variables in high dimension data. Furthermore, this proposed method also has the capability to improve the robustness in the regression model, especially when outliers are presence in the response variable or there is a heavy-tailed distribution in the error. Three algorithms were developed for the simulation of the modified non-transformed principal component and proposed adaptive penalized high dimension methods. In this study, the effectiveness of all the modified and proposed methods was examined through three simulation studies and also through the application of stock market price. It is known that the studies that perform variable selection, encouraging grouping effects and robustness in high dimensional stock market price using the statistical approach is still scarce. In conclusion, the modified and proposed high dimensional penalized methods provide much better performance results both for the simulation and real data application as compared to their counterpart.