Interpretable Vector AutoRegressions with Exogenous Time Series
This work addresses the problem of interpretability and estimation in large VARX models for practitioners in fields like marketing, though it is incremental as it builds on existing sparse estimation methods.
The authors tackled the challenge of estimating large VARX models, which incorporate exogenous variables, by proposing a lag-based hierarchically sparse estimator called HVARX. Their results show that HVARX provides a highly interpretable model and improves out-of-sample forecast accuracy compared to a lasso-type approach.
The Vector AutoRegressive (VAR) model is fundamental to the study of multivariate time series. Although VAR models are intensively investigated by many researchers, practitioners often show more interest in analyzing VARX models that incorporate the impact of unmodeled exogenous variables (X) into the VAR. However, since the parameter space grows quadratically with the number of time series, estimation quickly becomes challenging. While several proposals have been made to sparsely estimate large VAR models, the estimation of large VARX models is under-explored. Moreover, typically these sparse proposals involve a lasso-type penalty and do not incorporate lag selection into the estimation procedure. As a consequence, the resulting models may be difficult to interpret. In this paper, we propose a lag-based hierarchically sparse estimator, called "HVARX", for large VARX models. We illustrate the usefulness of HVARX on a cross-category management marketing application. Our results show how it provides a highly interpretable model, and improves out-of-sample forecast accuracy compared to a lasso-type approach.