Estimation of stationary autoregressive models with the Bayesian LASSO

Abstract

This article explores the problem of estimating stationary autoregressive models from observed data using the Bayesian least absolute shrinkage and selection operator (LASSO). By characterizing the model in terms of partial autocorrelations, rather than coefficients, it becomes straightforward to guarantee that the estimated models are stationary. The form of the negative log‐likelihood is exploited to derive simple expressions for the conditional likelihood functions, leading to efficient algorithms for computing the posterior mode by coordinate‐wise descent and exploring the posterior distribution by Gibbs sampling. Both empirical Bayes and Bayesian methods are proposed for the estimation of the LASSO hyper‐parameter from the data. Simulations demonstrate that the Bayesian LASSO performs well in terms of prediction when compared with a standard autoregressive order selection method.

Bayesian Shrinkage Estimation of Time-varying Covariance Matrices in Financial Time Series

“…For the lasso parameter 𝜆, they considered using empirical Bayes by marginal likelihood or imposing gamma priors. For extensions and applications of lasso, we refer to Chen et al (2011), Guo et al (2012a), Schmidt and Makalic (2013), Benoit et al (2013) and Zhang and Biswas (2015).…”

An Ordered Lasso and Sparse Time-Lagged Regression

“…Nardi & Rinaldo (2011) studied the application of the standard lasso to the AR model and derived its asymptotic properties. Schmidt & Makalic (2013) suggested a Bayesian approach to the lasso based on the partial autocorrelation representation of AR models. In the following example, we compare coefficient estimates and order estimates among the ordered lasso, the lasso, and the standard AR fit.…”