Lux, Thomas, 1962- (2006) The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. (Working papers (Warwick Business School. Financial Econometrics Research Centre)).

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Abstract

Multifractal processes have recently been proposed as a new formalism for modelling the time series of returns in finance. The major attraction of these processes is their ability to generate various degrees of long memory in different powers of returns - a feature that has been found in virtually all financial data. Initial difficulties stemming from non-stationarity and the combinatorial nature of the original model have been overcome by the introduction of an iterative Markov-switching multifractal model in Calvet and Fisher (2001) which allows for estimation of its parameters via maximum likelihood and Bayesian forecasting of volatility. However, applicability of MLE is restricted to cases with a discrete distribution of volatility components. From a practical point of view, ML also becomes computationally unfeasible for large numbers of components even if they are drawn from a discrete distribution. Here we propose an alternative GMM estimator together with linear forecasts which in principle is applicable for any continuous distribution with any number of volatility components. Monte Carlo studies show that GMM performs reasonably well for the popular Binomial and Lognormal models and that the loss incurred with linear compared to optimal forecasts is small. Extending the number of volatility components beyond what is feasible with MLE leads to gains in forecasting accuracy for some time series.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre Faculty of Social Sciences > Warwick Business School
Library of Congress Subject Headings (LCSH):	Economic forecasting, Markov processes, Bayesian statistical decision theory, Moments method (Statistics)
Series Name:	Working papers (Warwick Business School. Financial Econometrics Research Centre)
Publisher:	Warwick Business School, Financial Econometrics Research Centre
Place of Publication:	Coventry
Date:	5 April 2006
Number:	No.06-
Number of Pages:	43
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Andersen, T.G. and T. Bollerslev (1997) Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long Run in High Frequency Data,Journal of Finance, 52, 975-1005. Andersen, T.G. and B.E. S(rensen (1996) GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study, Journal of Business and Economics Statistics, 14, 328-352. Baillie, R.T., T. Bollerslev and H.O. Mikkelsen (1996) Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 74, 3-30. Beran, J. (1994) Statistics for Long-Memory Processes. New York: Chapman & Hall. Brockwell, P.J. and R. Dahlhaus (2004) Generalized Levinson-Durbin and Burg Algorithms, Journal of Econometrics, 118, 129-149. Brockwell, P.J. and R.A. Davis (1991) Time Series: Theory and Methods. New York, Springer. Calvet, L. and A. Fisher (2001) Forecasting Multifractal Volatility, Journal of Econometrics, 105, 27-58, working paper version: NYU Stern Working Paper FIN-99-017 (1999). Calvet, L. and A. Fisher (2002a) Multifractality in Asset Returns: Theory and Evidence, Review of Economics & Statistics, 84, 381-406. Calvet, L. and A. Fisher (2002b) Regime Switching and the Estimation of Multifractal Processes, Mimeo: Harvard University. Calvet, L. and A. Fisher (2004) Regime Switching and the Estimation of Multifractal Processes,Journal of Financial Econometrics, 2,49-83. Calvet, L., A. Fisher and B.Mandelbrot (1997) Cowles Foundation Discussion Papers no. 1164-1166, Yale University, available at http://www.ssrn.com. Calvet, L., A. Fisher and S. Thompson (2006) Volatility Comovement: A Multi-Frequency Approach, Journal of Econometrics, 131, 179-215. Chung, C.-F. (2002) Estimating the Fractionally Integrated GARCH Model. Mimeo: Academia Sinica. Diebold, F. and R. Mariano (1995) Comparing Predictive Accurancy, Journal of Business and Economics Statistics, 13, 253-263. Ding, Z., C.W.J. Granger and R.F.Engle (1993) A Long Memory Property of Stock Market Returns and a New Model, Journal of Empirical Finance, 1, 83-106. Hansen, L.P (1982) Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50, 1029-1054. Hansen, L.P., J. Heaton and A. Yaron (1996) Finite-Sample Properties of Some Alternative GMM Estimators, Journal of Business & Economics Statistics, 14, 262-280. Harris, D. and L. M´aty´as (1999) Introduction to the Generalized Method of Moments Estimation, Chap. 1 in: L. M´aty´as, ed., Generalized Method of Moments Estimation, Cambridge: University Press. Lobato, I.N. and N.E. Savin (1998) Real and Spurious Long-Memory Properties of Stock Market Data, Journal of Business & Economics Statistics, 16, 261-283. Mandelbrot, B. (1974) Intermittent Turbulence in Self Similar Cascades: Divergence of High Moments and Dimension of Carrier, Journal of Fluid Mechanics, 62, 331-358. Poon, S.-H. and C. Granger (2003) Forecasting Volatility in Financial Markets: A Review, Journal of Economic Literature, 41, 468-539. Vassilicos, J.C., A. Demos and F. Tata (1993) No Evidence of Chaos But Some Evidence of Multifractals in the Foreign Exchange and the Stock Market, in: Crilly, A.J., R.A Earnshaw and H. Jones, eds., Applications of Fractals and Chaos. Berlin: Springer. Vilasuso, J. (2002) Forecasting Exchange Rate Volatility, Economics Letters, 76, 59-64. Zumbach, G. (2004) Volatility Process and Volatility Forecast with Long Memory, Quantitative Finance, 4, 70-86.
URI:	http://wrap.warwick.ac.uk/id/eprint/1749

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