Bayesian Variance Changepoint Detection in Linear Models with Symmetric Heavy-Tailed Errors

Normality and static variance are very common assumptions in traditional financial theories and risk modeling for mathematical convenience. Empirical evidence suggests otherwise. With the rapid growth in volatility-based financial innovations and market, it is beneficial and essential to look beyond the traditional restrictive assumptions. This paper discusses Bayesian analysis of the variance changepoints problem in linear models with flexible error distributions. Specifically, we consider the class of scale mixtures of normal distributions, which not only exhibits symmetric heavy-tailed behavior, but also includes many common error distributions as special cases, such as the normal and Student-t distributions. Our proposed approach can reduce the influence of atypical observations and thus offer a robust technique for detecting the variance changepoints in many financial and economic data. We propose an efficient Gibbs sampling procedure to generate posterior samples and in turn to perform Bayesian inference. Simulation studies are conducted to demonstrate satisfactory performance of the proposed methodology. The closing price data set from the US stocks database is analyzed for illustrative purposes.