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Generalized Method of Moment estimation of multivariate multifractal models

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  • Liu, Ruipeng
  • Lux, Thomas

Abstract

Multifractal processes have recently been introduced as a new tool for modeling the stylized facts of financial markets and have been found to consistently provide certain gains in performance over basic volatility models for a broad range of assets and for various risk management purposes. Due to computational constraints, multivariate extensions of the baseline univariate multifractal framework are, however, still very sparse so far. In this paper, we introduce a parsimoniously designed multivariate multifractal model, and we implement its estimation via a Generalized Methods of Moments (GMM) algorithm. Monte Carlo studies show that the performance of this GMM estimator for bivariate and trivariate models is similar to GMM estimation for univariate multifractal models. An empirical application shows that the multivariate multifractal model improves upon the volatility forecasts of multivariate GARCH over medium to long forecast horizons.

Suggested Citation

  • Liu, Ruipeng & Lux, Thomas, 2017. "Generalized Method of Moment estimation of multivariate multifractal models," Economic Modelling, Elsevier, vol. 67(C), pages 136-148.
    • Handle: RePEc:eee:ecmode:v:67:y:2017:i:c:p:136-148
    DOI: 10.1016/j.econmod.2016.11.010
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    References listed on IDEAS

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    Cited by:

    1. Lux, Thomas, 2022. "Inference for Nonlinear State Space Models: A Comparison of Different Methods applied to Markov-Switching Multifractal Models," Econometrics and Statistics, Elsevier, vol. 21(C), pages 69-95.
    2. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    3. Lux, Thomas, 2018. "Inference for nonlinear state space models: A comparison of different methods applied to Markov-switching multifractal models," Economics Working Papers 2018-07, Christian-Albrechts-University of Kiel, Department of Economics.

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    More about this item

    Keywords

    Multivariate; Multifractal; Long memory; GMM estimation;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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