2012/08/15 by Filip Zikes, Filip Žikeš, Jozef Baruník +5
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Economics and business #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Statistical Finance (q-fin.ST) #q-fin.ST
paper · pdf · doi:10.48550/arxiv.1208.3087
openalex publication_date 2012/08/15 · arxiv created 2013/04/02 · arxiv updated 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 β-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.