Lux, Thomas (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) (No.06-).

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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
Official Date:	5 April 2006
Dates:	Date Event 5 April 2006 Published
Number:	No.06-
Number of Pages:	43
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access

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