Large vector autoregressive exogenous factor (VARX) model with network regularization

The vector autoregressive model has long been used for portfolio analysis, while a recent extension (VARX) incorporates exogenous factors. Despite its increased forecasting precision, the applicability of the VARX model is seriously hampered in the absence of sparsity, as the number of coefficients to be estimated grows quadratically with the number of series. We introduce a novel regularization method for the VARX model in the context of portfolios, where weighted links between portfolios are used to construct a penalty function for the autoregressive parameter matrixes. To test the prediction performance of the new method, we first cluster the time series into several groups using wavelet decomposition and hierarchical clustering, after which we construct data sets of different homogeneity. Our method is advantageous in two ways: the computation time for the model is significantly reduced, and the forecasting precision of the model is enhanced by 50% compared with existing regularization methods.