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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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    References listed on IDEAS

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    Cited by:

    1. Javier Mencía & Enrique Sentana, 2018. "Volatility-Related Exchange Traded Assets: An Econometric Investigation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 599-614, October.
    2. Liu, Xiaochun, 2015. "Modeling time-varying skewness via decomposition for out-of-sample forecast," International Journal of Forecasting, Elsevier, vol. 31(2), pages 296-311.
    3. 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).
    4. Sucarrat, Genaro & Grønneberg, Steffen & Escribano, Alvaro, 2016. "Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 582-594.
    5. Leschinski, Christian, 2017. "On the memory of products of long range dependent time series," Economics Letters, Elsevier, vol. 153(C), pages 72-76.
    6. Antonio Cosma & Fausto Galli, 2006. "A Nonparametric ACD Model," LSF Research Working Paper Series 06-10, Luxembourg School of Finance, University of Luxembourg.
    7. Sucarrat, Genaro & Escribano, Alvaro, 2013. "Unbiased QML Estimation of Log-GARCH Models in the Presence of Zero Returns," MPRA Paper 50699, University Library of Munich, Germany.
    8. 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, New Economic School (NES).
    9. Cipollini, Fabrizio & Gallo, Giampiero M., 2019. "Modeling Euro STOXX 50 volatility with common and market-specific components," Econometrics and Statistics, Elsevier, vol. 11(C), pages 22-42.
    10. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    11. Alketa Bejko & Etleva Peta & Belinda Xarba, 2015. "The Evaluation of the Drafting Process of Regional’s Development Strategies in Albania. the Research on Gjirokastra’s Region," European Journal of Interdisciplinary Studies Articles, Revistia Research and Publishing, vol. 1, ejis_v1_i.
    12. Kim, Jiwon & Mahmassani, Hani S., 2015. "Compound Gamma representation for modeling travel time variability in a traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 40-63.
    13. 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".
    14. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. G.M. Gallo & D. Lacava & E. Otranto, 2020. "Measuring the Effects of Unconventional Policies on Stock Market Volatility," Working Paper CRENoS 202006, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
    16. 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.
    17. Sucarrat, Genaro & Grønneberg, Steffen, 2016. "Models of Financial Return With Time-Varying Zero Probability," MPRA Paper 68931, University Library of Munich, Germany.
    18. Fabrizio Cipollini & Giampiero M Gallo & Alessandro Palandri, 2020. "Realized Variance Modeling: Decoupling Forecasting from Estimation," Journal of Financial Econometrics, Oxford University Press, vol. 18(3), pages 532-555.
    19. 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.
    20. Demetrio Lacava & Giampiero M. Gallo & Edoardo Otranto, 2022. "Unconventional policies effects on stock market volatility: The MAP approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1245-1265, November.
    21. Giampiero M. Gallo & Edoardo Otranto, 2012. "Volatility Swings in the US Financial Markets," Econometrics Working Papers Archive 2012_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Jul 2012.
    22. 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.
    23. Stanislav Anatolyev, 2013. "Objects of nonstructural time series modeling (in Russian)," Quantile, Quantile, issue 11, pages 1-12, December.
    24. Amendola, Alessandra & Candila, Vincenzo & Gallo, Giampiero M., 2019. "On the asymmetric impact of macro–variables on volatility," Economic Modelling, Elsevier, vol. 76(C), pages 135-152.

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    More about this item

    Keywords

    Multiplicative Error Models; Realized Volatility; Financial Time Series; Composite MEM;
    All these keywords.

    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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