# Model selection for high-dimensional linear regression with dependent observations

## TL;DR

This paper studies the effectiveness of the orthogonal greedy algorithm (OGA) combined with a high-dimensional AIC for model selection in high-dimensional linear regression with dependent data, achieving optimal prediction rates.

## Contribution

It introduces a novel combination of OGA and HDAIC that attains optimal convergence rates without prior sparsity knowledge.

## Key findings

- OGA with HDAIC achieves optimal convergence rates.
- The method prevents overfitting in high-dimensional settings.
- Applicable to models with dependent observations.

## Abstract

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike's information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.