Markov regime-switching autoregressive model with tempered stable distribution: simulation evidence

Markov regime-switching (MRS) autoregressive model is a widely used approach to model the economic and financial data with potential structural breaks. The innovation series of such MRS-type models are usually assumed to follow a Normal distribution, which cannot accommodate fat-tailed properties commonly present in empirical data. Many theoretical studies suggest that this issue can lead to inconsistent estimates. In this paper, we consider the tempered stable distribution, which has the attractive stability under aggregation property missed in other popular alternatives like Student's t-distribution and General Error Distribution (GED). Through systematically designed simulation studies with the MRS autoregressive models, our results demonstrate that the model with tempered stable distribution uniformly outperforms those with Student's t-distribution and GED. Our empirical study on the implied volatility of the S&P 500 options (VIX) also leads to the same conclusions. Therefore, we argue that the tempered stable distribution could be widely used for modelling economic and financial data in general contexts with an MRS-type specification.