# Lag selection and estimation of stable parameters for multiple autoregressive processes through convex programming

arXiv: https://arxiv.org/abs/2303.02114 · HTML: https://mlsanity.com/paper/2303.02114/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 17 references that are in the map.
- First posted on arXiv 3 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations](https://mlsanity.com/paper/1912.09002/) (2019)

## Abstract (arXiv)

Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have become available very recently. We, instead, consider multiple stable autoregressive processes that share an unknown lag. We use information across the different processes to simultaneously select the lag and estimate the parameters. We prove that the estimated process is stable, and we establish rates for the forecasting error that can outmatch the known rate in our setting. Our insights on the lag selection and the stability are also of interest for the case of individual autoregressive processes.