Froecast the USA Stock Indices with GARCH-type Models

GARCH-type models have been highly developed since Engle [1982] presented ARCH process 30 years ago. Different kinds of GARCH-type models are applicable to different kinds of research purposes. As documented by many literatures that short-memory processes with level shifts will exhibit properties that make standard tools conclude long-memory is present. Therefore, in this paper, we want to forecast with GARCH-type models and consider structural breaks and the long-memory characteristic. We analyze structural breaks and use the FIGARCH [Baillie et al., 1996] model comparing with GARCH [Bollerslev, 1986] model and EGARCH [Nelson, 1991] model to forecast the conditional variance process of three USA stock indices: Dow Jones Industrials Average (DJIA) index, Standard & Poor 500 (S&P 500) index and NASDAQ Composite (NASDAQ) index by using different in-sample size, different error distributions and forecasting different steps. We find the FIGARCH model is sensitive to the changes of conditions, and forecast better than the other two GARCH-type models.