Modeling Hong Kong’s stock index with the Student t‐mixture autoregressive model

It is well known that financial returns are usually not normally distributed, but rather exhibit excess kurtosis. This implies that there is greater probability mass at the tails of the marginal or conditional distribution. Mixture‐type time series models are potentially useful for modeling financial returns. However, most of these models make the assumption that the return series in each component is conditionally Gaussian, which may result in underestimates of the occurrence of extreme financial events, such as market crashes. In this paper, we apply the class of Student t‐mixture autoregressive (TMAR) models to the return series of the Hong Kong Hang Seng Index. A TMAR model consists of a mixture of g autoregressive components with Student t‐error distributions. Several interesting properties make the TMAR process a promising candidate for financial time series modeling. These models are able to capture serial correlations, time‐varying means and volatilities, and the shape of the conditional distributions can be time‐varied from short‐ to long‐tailed or from unimodal to multi‐modal. The use of Student t‐distributed errors in each component of the model allows for conditional leptokurtic distribution, which can account for the commonly observed unconditional kurtosis in financial data.