StMAR Toolbox: A MATLAB Toolbox for Student's t Mixture Autoregressive Models

Abstract

This document provides an overview of the StMAR Toolbox, a MATLAB toolbox specifically designed for simulation, estimation, diagnostic, and forecasting of the Student’s t mixture autoregressive (StMAR) model proposed by Meitz, Preve & Saikkonen (2018). The StMAR model is a new type of mixture autoregressive model with observation dependent mixing weights. Its stationary formulation implies that both the conditional and unconditional distributions of its AR component models are Student’s t, and that the conditional variances of these models are of ARCH type. The conditional and unconditional distributions of the StMAR model are both mixtures of Student’s t distributions. This makes it suitable for modelling time series with excess kurtosis, regime switching, multimodality, persistence, and conditional heteroskedasticity. Potential applications in finance include the modelling and forecasting of return, interest rate, and volatility proxy series, but researchers and practitioners from other fields can also use the toolbox without any modifications. The StMAR Toolbox is free and publicly available software.

Keywords: Mixture Model, Regime Switching, Conditional Heteroskedasticity, Student’s t Distribution, Financial Econometrics, Numerical Optimization, Parallel Computing, MATLAB

JEL Classification: C22, C46, C53, C58, C61, C63, C87