Long-term dependence with asymmetric conditional heteroscedasticity in stock returns

This paper studies the long-term dependence and the possible asymmetric behavior of the financial time series. Both can be modeled using a fractionally integrated autoregressive moving average time series model with threshold-type conditional heteroscedasticity, denoted as an ARFIMA-TGARCH model, into which a Bayesian approach is introduced to conduct the parameter estimation. With these parameters, we apply the ARFIMA-TGARCH model to describe the daily stock returns of six markets. From the empirical results, we find that the returns of these markets exhibit mildly long-memory processes and reveal an asymmetric response to the negative and positive news.