ARMAr-LASSO: Mitigating the Impact of Predictor Serial Correlation on the LASSO

TL;DR

This paper introduces ARMAr-LASSO, a novel method that pre-whitens predictors with ARMA filters to mitigate predictor serial correlation effects, improving estimation and forecasting in sparse linear time series models.

Contribution

The paper proposes ARMAr-LASSO, a new approach combining ARMA filtering with LASSO to address serial correlation issues in predictors, with theoretical guarantees and practical validation.

Findings

ARMAr-LASSO reduces estimation errors in sparse models with serially correlated predictors.

The method outperforms standard LASSO in forecasting accuracy on macroeconomic data.

Theoretical results support the effectiveness of pre-whitening in sparse time series modeling.

Abstract

We explore estimation and forecast accuracy for sparse linear models, focusing on scenarios where both predictors and errors carry serial correlations. We establish a clear link between predictor serial correlation and the performance of the LASSO, showing that even orthogonal or weakly correlated stationary AR processes can lead to significant spurious correlations due to their serial correlations. To address this challenge, we propose a novel approach named ARMAr-LASSO ({\em ARMA residuals LASSO}), which applies the LASSO to predictors that have been pre-whitened with ARMA filters and lags of dependent variable. We derive both asymptotic results and oracle inequalities for the ARMAr-LASSO, demonstrating that it effectively reduces estimation errors while also providing an effective forecasting and feature selection strategy. Our findings are supported by extensive simulations and an application to real-world macroeconomic data, which highlight the superior performance of the ARMAr-LASSO for handling sparse linear models in the context of time series.