A Novel Approach to Forecasting High Dimensional S&P500 Portfolio Using VARX Model with Information Complexity

This study considers vector autoregressive models that allow for endogenous and exogeneous regressors VARX using multivariate OLS regression. For the model selection, we follow bozdogan’s entropic or information-theoretic measure of complexity ICOMP criterion of the estimated inverse Fisher information matrix IFIM in choosing the best VARX lag parameter and we established that ICOMP outperform the conventional information criteria. As an empirical illustration, we reduced the dimension of the S&P500 multivariate time series using Sparse Principal Component Analysis (SPCA) and chose the best subset of 37 stocks belonging to six sectors. We then performed a portfolio of stocks based on the highest SPC loading weight matrix, plus the S&P500 index. Furthermore, we applied the proposed VARX model to predict the price movements in the constructed portfolio, where the S&P500 index was treated as an exogeneous regressor of the VARX model. It has been deduced too that the buy-sell decision making in response to VARX (4,0) for a stock outperforms investing and holding the stock over the out-of-sample period.