# Structured Estimation of Heterogeneous Time Series

arXiv: https://arxiv.org/abs/2311.08658 · HTML: https://mlsanity.com/paper/2311.08658/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 67 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [Evaluating time series forecasting models: An empirical study on performance estimation methods](https://mlsanity.com/paper/1905.11744/) (2019)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [The Gaussian Graphical Model in Cross-sectional and Time-series Data](https://mlsanity.com/paper/1609.04156/) (2016)
- [A critical review of LASSO and its derivatives for variable selection under dependence among covariates](https://mlsanity.com/paper/2012.11470/) (2020)
- [Regression modeling on stratified data with the lasso](https://mlsanity.com/paper/1508.05476/) (2015)
- [Penalized Estimation and Forecasting of Multiple Subject Intensive Longitudinal Data](https://mlsanity.com/paper/2007.05052/) (2020)

## Abstract (arXiv)

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).