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A Model for Multivariate Non-negative Valued Processes in Financial Econometrics

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Abstract

The Multiplicative Error Model introduced by Engle (2002) for non-negative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support. In this paper we propose a multivariate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated. The estimation procedure is hindered by the lack of probability density functions for multivariate non-negative valued random variables. We suggest the use of copula functions to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate the feasibility of the procedure and the gains over the equation by equation approach using a four variable fully interdependent model with different volatility measures.

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  • Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2007. "A Model for Multivariate Non-negative Valued Processes in Financial Econometrics," Econometrics Working Papers Archive wp2007_16, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  • Handle: RePEc:fir:econom:wp2007_16
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    Cited by:

    1. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2013. "Semiparametric Vector Mem," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1067-1086, November.
    2. Matteo Barigozzi & Brownlees Christian & Gallo Giampiero & David Veredas, "undated". "Disentangling systematic and idiosyncratic risks for large panels of assets," ULB Institutional Repository 2013/136237, ULB -- Universite Libre de Bruxelles.
    3. Bodnar, Taras & Hautsch, Nikolaus, 2016. "Dynamic conditional correlation multiplicative error processes," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 41-67.
    4. Ng, F.C. & Li, W.K. & Yu, Philip L.H., 2016. "Diagnostic checking of the vector multiplicative error model," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 86-97.
    5. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    6. 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.
    7. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.
    8. Cipollini, Fabrizio & Gallo, Giampiero M., 2010. "Automated variable selection in vector multiplicative error models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2470-2486, November.
    9. Heejoon Han & Myung D. Park, 2013. "Comparison of Realized Measure and Implied Volatility in Forecasting Volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(6), pages 522-533, September.
    10. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    11. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    12. 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.
    13. Anatolyev, Stanislav & Gospodinov, Nikolay, 2015. "Multivariate return decomposition: theory and implications," FRB Atlanta Working Paper 2015-7, Federal Reserve Bank of Atlanta.
    14. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, "undated". "Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility," CREATES Research Papers 2010-13, Department of Economics and Business Economics, Aarhus University.
    15. Taylor, Nick & Xu, Yongdeng, 2013. "The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data," Cardiff Economics Working Papers E2013/7, Cardiff University, Cardiff Business School, Economics Section.

    More about this item

    Keywords

    Volatility; Copula functions; Forecasting; GARCH; 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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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