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Vector Multiplicative Error Models: Representation and Inference

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The Multiplicative Error Model introduced by Engle (2002) for positive 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 positive valued random variables. We suggest the use of copula functions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes. Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2006_15.

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Length: 55
Date of creation: Oct 2006
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Handle: RePEc:fir:econom:wp2006_15

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  1. Robert F. Engle & Giampiero M. Gallo, 2003. "A Multiple Indicators Model for Volatility Using Intra-Daily Data," NBER Working Papers 10117, National Bureau of Economic Research, Inc.
  2. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
  3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  4. Bent Jørgensen & Sven Jesper Knudsen, 2004. "Parameter Orthogonality and Bias Adjustment for Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114.
  5. Manganelli, Simone, 2002. "Duration, volume and volatility impact of trades," Working Paper Series 0125, European Central Bank.
  6. Peter Xue-Kun Song, 2000. "Multivariate Dispersion Models Generated From Gaussian Copula," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  8. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  9. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  10. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  11. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
  12. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
  13. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-82, June.
  14. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
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Cited by:
  1. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2014. "Disentangling Systematic and Idiosyncratic Dynamics in Panels of Volatility Measures," Econometrics Working Papers Archive 2014_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
  2. Drew Creal & Siem Jan Koopman & Andr� Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
  3. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2013. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 12(1), pages 89-121, December.
  4. Nikolaus Hautsch, 2007. "Capturing Common Components in High-Frequency Financial Time Series: A Multivariate Stochastic Multiplicative Error Model," SFB 649 Discussion Papers SFB649DP2007-052, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. Ahoniemi, Katja & Lanne, Markku, 2007. "Joint Modeling of Call and Put Implied Volatility," MPRA Paper 6318, University Library of Munich, Germany.
  6. Christian T. Brownlees & Giampiero Gallo, 2008. "Comparison of Volatility Measures: a Risk Management Perspective," Econometrics Working Papers Archive wp2008_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  7. Daniel Preve & Anders Eriksson & Jun Yu, 2009. "Forecasting Realized Volatility Using A Nonnegative Semiparametric Model," Finance Working Papers 23049, East Asian Bureau of Economic Research.
  8. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2009. "Semiparametric vector MEM," Econometrics Working Papers Archive wp2009_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  9. Nikolaus Hautsch & Vahidin Jeleskovic, 2008. "Modelling High-Frequency Volatility and Liquidity Using Multiplicative Error Models," SFB 649 Discussion Papers SFB649DP2008-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  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. Drew Creal & Siem Jan Koopman & Andr� Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute.
  12. Taras Bodnar & Nikolaus Hautsch, 2012. "Copula-Based Dynamic Conditional Correlation Multiplicative Error Processes," SFB 649 Discussion Papers SFB649DP2012-044, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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