Forecasting financial market activity using a semiparametric fractionally integrated Log-ACD

This paper discusses forecasting of long memory and a nonparametric scale function in nonnegative financial processes based on a fractionally integrated Log-ACD (FI-Log-ACD) and its semiparametric extension (Semi-FI-Log-ACD). Necessary and sufficient conditions for the existence of a stationary solution of the FI-Log-ACD are obtained. Properties of this model under log-normal assumption are summarized. A linear predictor based on the truncated AR(oo) form of the logarithmic process is proposed. It is shown that this proposal is an approximately best linear predictor. Approximate variances of the prediction errors for an individual observation and for the conditional mean are obtained. Forecasting intervals for these quantities in the log- and the original processes are calculated under log-normal assumption. The proposals are applied to forecasting daily trading volumes and daily trading numbers in financial market.