Abstract
ABSTRACTThis article 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 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. The results of the comparison show that the MSMD and the Long Memory Stochastic Duration model perform similarly and are superior to the short-memory Autoregressive Conditional Duration models.
Highlights
Financial durations measure the time elapsed between various financial market events related to transactions arrivals, price fluctuations, or trading volumes
Since the mean of the standardized durations is, by construction, close to one, we impose this restriction in all models and do not report the estimates of the various constant terms
This paper introduces a new model for financial durations, featuring persistence that translates from durations to realized volatility
Summary
Financial durations measure the time elapsed between various financial market events related to transactions arrivals, price fluctuations, or trading volumes. Deo, Hsieh & Hurvich (2010) recently test for long memory in durations and the associated counts and find significant evidence to support the presence of long memory in durations. Ever since the seminal contribution of Engle & Russell (1998), who introduced the first time-series model for financial durations, a number of studies have documented the slowly decaying autocorrelation function of transaction, price and volume durations; see Pacurar (2008) for a detailed literature review. Despite this empirical regularity, there is currently no paper that explores the alternative models for capturing the persistent autocorrelations of durations and its implications for forecasting.
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