Modeling and Forecasting Persistent Financial Durations

Although the MSMD process is exponential β-mixing as we show in the article, it is capable of generating highly persistent autocorrelation. We study, analytically and by simulation, how this feature of durations generated by the MSMD process propagates to counts and realized volatility.

We employ a quasi-maximum likelihood estimator of the MSMD parameters based on the Whittle approximation and establish its strong consistency and asymptotic normality for general MSMD specifications. We show that the Whittle estimation is a computationally simple and fast alternative to maximum likelihood. Finally, we compare the performance of the MSMD model with competing short- and long-memory duration models in an out-of-sample forecasting exercise based on price durations of three major foreign exchange futures contracts.