A Bayesian Mixture of Lasso Regressions with t-Errors

TL;DR

This paper introduces a Bayesian mixture of lasso regressions with t-distributed errors, designed for financial data with outliers and skewness, utilizing advanced PMCMC algorithms for fitting.

Contribution

It develops a novel Bayesian mixture model with t-errors and sparse variable selection, combined with a state-of-the-art PMCMC algorithm for complex financial data analysis.

Findings

Model effectively captures outliers and skewness in financial data.

The PMCMC algorithm successfully fits the complex mixture model.

Empirical results demonstrate improved clustering and variable selection.

Abstract

Motivated by a challenging problem in financial trading we are presented with a mixture of regressions with variable selection problem. In this regard, one is faced with data which possess outliers, skewness and, simultaneously, due to the nature of financial trading, one would like to be able to construct clusters with specific predictors that are fairly sparse. We develop a Bayesian mixture of lasso regressions with $t-$errors to reflect these specific demands. The resulting model is necessarily complex and to fit the model to real data, we develop a state-of-the-art Particle Markov chain Monte Carlo (PMCMC) algorithm based upon sequential Monte Carlo (SMC) methods. The model and algorithm are investigated on both simulated and real data.