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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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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. 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, Elsevier, vol. 1(1), pages 83-106, June.
  2. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, Elsevier, vol. 8(4), pages 377-399, November.
  3. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, Elsevier, vol. 131(1-2), pages 3-27.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  5. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 579-625, March.
  7. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  8. 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, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114.
  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, Federal Reserve Bank of Minneapolis 157, Federal Reserve Bank of Minneapolis.
  10. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford.
  11. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
  12. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 37(3), pages 561-82, June.
  13. 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, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 305-320.
  14. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
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Cited by:
  1. Hautsch, Nikolaus, 2007. "Capturing common components in high-frequency financial time series: A multivariate stochastic multiplicative error model," CFS Working Paper Series 2007/25, Center for Financial Studies (CFS).
  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. Ahoniemi, Katja & Lanne, Markku, 2007. "Joint Modeling of Call and Put Implied Volatility," MPRA Paper 6318, University Library of Munich, Germany.
  4. 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).
  5. 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.
  6. 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, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" 2014_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
  7. 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.
  8. Christian T. Brownlees & Giampiero Gallo, 2008. "Comparison of Volatility Measures: a Risk Management Perspective," Econometrics Working Papers Archive, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" wp2008_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  9. Daniel PREVE & Anders ERIKSSON & Jun YU, 2009. "Forecasting Realized Volatility Using A Nonnegative Semiparametric Model," Working Papers, Singapore Management University, School of Economics 22-2009, Singapore Management University, School of Economics.
  10. repec:dgr:uvatin:2008108 is not listed on IDEAS
  11. 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.
  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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