# Modeling and Forecasting Persistent Financial Durations

## Author Info

• Filip Zikes
• Jozef Barunik
• Nikhil Shenai

## 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.

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File URL: http://arxiv.org/pdf/1208.3087

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1208.3087.

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Date of revision: Apr 2013
Handle: RePEc:arx:papers:1208.3087

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Web page: http://arxiv.org/

## Related research

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## References

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1. Fernandes, Marcelo & Grammig, Joachim, 2002. "A Family of Autoregressive Conditional Duration Models," Economics Working Papers (Ensaios Economicos da EPGE) 440, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
2. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
3. Fei Chen & Francis X. Diebold & Frank Schorfheide, 2012. "A Markov-Switching Multi-Fractal Inter-Trade Duration Model, with Application to U.S. Equities," NBER Working Papers 18078, National Bureau of Economic Research, Inc.
4. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2009. "Duration-Based Volatility Estimation," Global COE Hi-Stat Discussion Paper Series gd08-034, Institute of Economic Research, Hitotsubashi University.
5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
6. Michael R. King & Carol Osler & Dagfinn Rime, 2011. "Foreign exchange market structure, players and evolution," Working Paper 2011/10, Norges Bank.
7. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
8. Lux, Thomas, 2008. "The Markov-Switching Multifractal Model of Asset Returns: GMM Estimation and Linear Forecasting of Volatility," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 194-210, April.
9. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
10. Deo, Rohit & Hurvich, Clifford M. & Soulier, Philippe & Wang, Yi, 2009. "Conditions For The Propagation Of Memory Parameter From Durations To Counts And Realized Volatility," Econometric Theory, Cambridge University Press, vol. 25(03), pages 764-792, June.
11. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
12. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 382-416, April.
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