Forecasting volatility and volume in the Tokyo Stock Market: Long memory, fractality and regime switching

We investigate the predictability of both volatility and volume for a large sample of Japanese stocks. The particular emphasis of this paper is on assessing the performance of long memory time series models in comparison to their short-memory counterparts. Since long memory models should have a particular advantage over long forecasting horizons, we consider predictions of up to 100 days ahead. In most respects, the long memory models (ARFIMA, FIGARCH and the recently introduced multifractal model) dominate over GARCH and ARMA models. However, while FIGARCH and ARFIMA also have quite a number of cases with dramatic failures of their forecasts, the multifractal model does not suffer from this shortcoming and its performance practically always improves upon the naïve forecast provided by historical volatility. As a somewhat surprising result, we also find that, for FIGARCH and ARFIMA models, pooled estimates (i.e. averages of parameter estimates from a sample of time series) give much better results than individually estimated models.