A Mixture Autoregressive Model Based on Student's t-Distribution
23 Pages Posted: 24 May 2018 Last revised: 11 Aug 2021
Date Written: Aug 20, 2018
A new mixture autoregressive model based on Student’s t-distribution is proposed. A key feature of our model is that the conditional t-distributions of the component models are based on autoregressions that have multivariate t-distributions as their (low-dimensional) stationary distributions. That autoregressions with such stationary distributions exist is not immediate. Our formulation implies that the conditional mean of each component model is a linear function of past observations and the conditional variance is also time varying. Compared to previous mixture autoregressive models our model may therefore be useful in applications where the data exhibits rather strong conditional heteroskedasticity. Our formulation also has the theoretical advantage that conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. An empirical example employing a realized kernel series constructed from S&P 500 high-frequency intraday data shows that the proposed model performs well in volatility forecasting. Our methodology is implemented in the freely available StMAR Toolbox for MATLAB.
Keywords: Conditional heteroskedasticity, mixture model, regime switching, Student’s t-distribution
JEL Classification: C22, C51, C58
Suggested Citation: Suggested Citation