Large VARX Model With Network Regularization

Abstract

The vector autoregression model (VAR) has long been used for portfolio analysis, with recent extensions that incorporate exogenous factors (VARX). Despite its increased forecasting precision, the applicability of the VARX model is deeply hampered in the absence of sparsity, as the amount of coefficients to be estimated grows quadratically with the number of series. We introduce a novel regularization method for VARX model in the context of portfolios, where weighted links between portfolios are used to construct a penalty function for the autoregressive parameter matrices. 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 datasets of different homogeneity. Our method is meritorious from two perspectives: the computation time for the model is significantly reduced and the forecasting precision of the model is enhanced by fifty percent compared to existing regularization methods.

Keywords: Varx Model, Networks, Group Lasso, High-Dimensional Time Series, Forecasting, Time Series Clustering