Structured Estimation of Heterogeneous Time Series

TL;DR

This paper extends the multi-VAR approach for modeling heterogeneous multivariate time series by introducing adaptive weighting schemes that enhance estimation accuracy, demonstrated through simulations and practical examples.

Contribution

The work develops adaptive penalty weights for the multi-VAR framework, improving estimation performance in heterogeneous time series modeling.

Findings

Adaptive multi-VAR outperforms alternative estimators in simulations.

New weighting schemes reduce bias and improve path recovery.

Demonstrated utility with toy examples and R package implementation.

Abstract

How best to model structurally heterogeneous processes is a foundational question in the social, health and behavioral sciences. Recently, Fisher et al., (2022) introduced the multi-VAR approach for simultaneously estimating multiple-subject multivariate time series characterized by common and individualizing features using penalized estimation. This approach differs from many popular modeling approaches for multiple-subject time series in that qualitative and quantitative differences in a large number of individual dynamics are well-accommodated. The current work extends the multi-VAR framework to include new adaptive weighting schemes that greatly improve estimation performance. In a small set of simulation studies we compare adaptive multi-VAR with these new penalty weights to common alternative estimators in terms of path recovery and bias. Furthermore, we provide toy examples and code demonstrating the utility of multi-VAR under different heterogeneity regimes using the multivar package for R (Fisher, 2022).