How to Forecast Long-Run Volatility: Regime Switching and the Estimation of Multifractal Processes

By Calvet Laurent E. and Fisher Adlai J.
Journal of Financial Econometrics (2004)

  • Laurent E. Calvet

    HEC Paris


  • Adlai J. Fisher

    University of British Columbia



September 27, 2013

Last update

June 20, 2016










This code implements the Maximum-Likelihood (ML) estimation of a Markov-Switching Multifractal process. It focuses on the simple case where M is a binomial random variable taking values m0 or 2-m0 with equal probability. The full parameter vector is then (b, m0, γk, σ), where m0 characterizes the distribution of the multipliers, σ is the unconditional standard deviation of returns, and b and γk define the set of switching probabilities. User can provide starting values of ML optimization (optional) and choose the number of volatility frequencies (between 1 and 10), denoted kbar. Results display the four estimated parameters, the Log-Likelihood and some diagnostic information about the optimization procedure.

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