In Nicholson et al. (2021), we propose hierarchical lag structures, called “HLag”, that simultaneously perform dimension reduction through sparsity and incorporate the notion of lag order selection into a convex regularizer. Through macroeconomic, financial, and energy applications, we highlight Hlag’s forecasting improvements as well as its convenient, interpretable output.
Next, we extend the methodology to Vector AutoRegressive Moving Average (VARMA) models. In practice, identifiability issues have led many authors to abandon VARMA models in favor of the simpler VAR. Such a practice is unfortunate since even very simple VARMAs can have quite complicated VAR representations. In Wilms et al. (2019), we narrow this gap with a new optimization-based approach to VARMA identification that is built upon the principle of parsimony.
While VARs and VARMAs are cornerstones in multivariate time series analysis; they typically require all component series to enter the model at the same frequency. In practice, however, macro and financial series are typically recorded at different frequencies; quarterly, monthly, weekly or daily for instance. In Hecq et al. (2021), we therefore extend the HLag methodology to a Mixed-Frequency VAR framework.
The HLag estimator for VARs and VARMA are available in the R package bigtime, the package hierarchical-MFVAR tackles mixed-frequency models.