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Vector Multiplicative Error Models: Representation and Inference

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  • Fabrizio Cipollini
  • Robert F. Engle
  • Giampiero M. Gallo

Abstract

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 multi-variate 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 copulafunctions 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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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12690.

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Date of creation: Nov 2006
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Handle: RePEc:nbr:nberwo:12690

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  1. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  3. Manganelli, Simone, 2002. "Duration, volume and volatility impact of trades," Working Paper Series 0125, European Central Bank.
  4. 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.
  5. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  6. 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.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  8. 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.
  9. 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.
  10. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
  11. 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.
  12. 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.
  13. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  14. 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.
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Cited by:
  1. Daniel PREVE & Anders ERIKSSON & Jun YU, 2009. "Forecasting Realized Volatility Using A Nonnegative Semiparametric Model," Working Papers 22-2009, Singapore Management University, School of Economics.
  2. Ahoniemi, Katja & Lanne, Markku, 2009. "Joint modeling of call and put implied volatility," International Journal of Forecasting, Elsevier, vol. 25(2), pages 239-258.
  3. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2011. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series 2011/25, Center for Financial Studies (CFS).
  4. Drew Creal & Siem Jan Koopman & Andre Lucas, 2009. "A General Framework for Observation Driven Time-Varying Parameter Models," Global COE Hi-Stat Discussion Paper Series gd08-038, Institute of Economic Research, Hitotsubashi University.
  5. 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.
  6. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(1), pages 29-56, Winter.
  7. 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.
  8. 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.
  9. repec:dgr:uvatin:2008108 is not listed on IDEAS
  10. 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.
  11. 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".
  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.

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