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Multiplicative Error Models

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Abstract

Financial time series analysis has focused on data related to market trading activity. Next to the modeling of the conditional variance of returns within the GARCH family of models, recent attention has been devoted to other variables: first, and foremost, volatility measured on the basis of ultra-high frequency data, but also volumes, number of trades, durations. In this paper, we examine a class of models, named Multiplicative Error Models, which are particularly suited to model such non-negative time series. We discuss the univariate specification, by considering the base choices for the conditional expectation and the error term. We provide also a general framework, allowing for richer specifications of the conditional mean. The outcome is a novel MEM (called Composite MEM) which is reminiscent of the short- and long-run component GARCH model by Engle and Lee (1999). Inference issues are discussed relative to Maximum Likelihood and Generalized Method of Moments estimation. In the application, we show the regularity in parameter estimates and forecasting performance obtainable by applying the MEM to the realized kernel volatility of components of the S&P100 index. We suggest extensions of the base model by enlarging the information set and adopting a multivariate specification.

Suggested Citation

  • Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Multiplicative Error Models," Econometrics Working Papers Archive 2011_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Apr 2011.
  • Handle: RePEc:fir:econom:wp2011_03
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    Cited by:

    1. Markus Engler & Vahidin Jeleskovic, 2016. "Intraday volatility, trading volume and trading intensity in the interbank market e-MID," MAGKS Papers on Economics 201648, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    2. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 16(1), pages 129-154.
    3. repec:eur:ejisjr:41 is not listed on IDEAS
    4. Chen, Fei & Diebold, Francis X. & Schorfheide, Frank, 2013. "A Markov-switching multifractal inter-trade duration model, with application to US equities," Journal of Econometrics, Elsevier, vol. 177(2), pages 320-342.
    5. Heejoon Han & Myung D. Park & Shen Zhang, 2015. "A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(3), pages 209-219, April.
    6. COSMA, Antonio & GALLI, Fausto, 2006. "A nonparametric ACD model," CORE Discussion Papers 2006067, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Torben G. Andersen & Oleg Bondarenko & Albert S. Kyle & Anna Obizhaeva, 2016. "Intraday Trading Invariance in the E-mini S&P 500 Futures Market," Working Papers w0229, Center for Economic and Financial Research (CEFIR).
    8. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    9. Liu, Xiaochun, 2011. "Modeling the time-varying skewness via decomposition for out-of-sample forecast," MPRA Paper 41248, University Library of Munich, Germany.
    10. Mencía, Javier & Sentana, Enrique, 2015. "Volatility-related exchange traded assets: an econometric investigation," CEPR Discussion Papers 10444, C.E.P.R. Discussion Papers.
    11. Sucarrat, Genaro & Escribano, Álvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," UC3M Working papers. Economics we1321, Universidad Carlos III de Madrid. Departamento de Economía.
    12. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," CORE Discussion Papers 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    13. E. Otranto, 2012. "Spillover Effects in the Volatility of Financial Markets," Working Paper CRENoS 201217, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    14. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci De Magistris, 2014. "Chasing Volatility. A Persistent Multiplicative Error Model With Jumps," "Marco Fanno" Working Papers 0186, Dipartimento di Scienze Economiche "Marco Fanno".

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    Keywords

    Multiplicative Error Models; Realized Volatility; Financial Time Series; Composite MEM;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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