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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.

Suggested Citation

  • 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. Kul B. Luintel & Yongdeng Xu, 2017. "Testing weak exogeneity in multiplicative error models," Quantitative Finance, Taylor & Francis Journals, vol. 17(10), pages 1617-1630, October.
    3. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2010. "Disentangling Systematic and Idiosyncratic Risk for Large Panels of Assets," Econometrics Working Papers Archive wp2010_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    4. Bodnar, Taras & Hautsch, Nikolaus, 2016. "Dynamic conditional correlation multiplicative error processes," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 41-67.
    5. 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.
    6. 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.
    7. Huiling Yuan & Guodong Li & Junhui Wang, 2022. "High-Frequency-Based Volatility Model with Network Structure," Papers 2204.12933, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Stanislav Anatolyev & Nikolay Gospodinov, 2019. "Multivariate Return Decomposition: Theory and Implications," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 487-508, May.
    13. 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.
    14. 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.
    15. 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.
    16. Lien, Donald & Lee, Geul & Yang, Li & Zhang, Yuyin, 2018. "Volatility spillovers among the U.S. and Asian stock markets: A comparison between the periods of Asian currency crisis and subprime credit crisis," The North American Journal of Economics and Finance, Elsevier, vol. 46(C), pages 187-201.
    17. 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.
    18. N. Taylor & Y. Xu, 2017. "The logarithmic vector multiplicative error model: an application to high frequency NYSE stock data," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1021-1035, July.

    More about this item

    Keywords

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

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