Interpretable vector autoregressions with exogenous time series

Ines Wilms, Sumanta Basu, Jacob Bien, David S. Matteson

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


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.
Original languageEnglish
Title of host publicationInterpretable Machine Learning
Subtitle of host publicationNIPS 2017 symposium proceedings
EditorsAndrew Gordon Wilson, Jason Yosinski, Patrice Simard, Rich Caruana, William Herlands
Publication statusPublished - 2017
Externally publishedYes

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