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.