Modeling and Forecasting Persistent Financial Durations

TL;DR

This paper develops the MSMD model for financial durations, demonstrating its ability to generate persistent autocorrelation and outperform short-memory models in forecasting foreign exchange futures durations.

Contribution

The paper introduces the MSMD model for durations, adapts the MSM stochastic volatility framework, and provides a fast estimation method with strong theoretical properties.

Findings

MSMD generates highly persistent autocorrelation in durations.

MSMD outperforms short-memory models in out-of-sample forecasting.

Whittle estimation is efficient and consistent for MSMD parameters.

Abstract

This paper introduces the Markov-Switching Multifractal Duration (MSMD) model by adapting the MSM stochastic volatility model of Calvet and Fisher (2004) to the duration setting. Although the MSMD process is exponential $\beta$-mixing as we show in the paper, 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. The results of the comparison show that the MSMD and LMSD perform similarly and are superior to the short-memory ACD models.