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Vector Multiplicative Error Models: Representation and Inference

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Author Info
Fabrizio Cipollini
Robert F. Engle
Giampiero M. Gallo

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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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C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Neil Shephard, 1995. "Generalized linear autoregressions," Economics Papers 8., Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  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. Manganelli, Simone, 2005. "Duration, volume and volatility impact of trades," Journal of Financial Markets, Elsevier, vol. 8(4), pages 377-399, November. [Downloadable!] (restricted)
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  4. 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. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March. [Downloadable!] (restricted)
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  7. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
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  9. 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.
  10. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  11. 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 and Swedish Statistical Association, vol. 27(2), pages 305-320. [Downloadable!] (restricted)
  12. 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 and Swedish Statistical Association, vol. 31(1), pages 93-114. [Downloadable!] (restricted)
  13. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446. [Downloadable!]
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  1. Nikolaus Hautsch, 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. [Downloadable!]
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  2. Drew Creal & Siem Jan Koopman & André Lucas, 2008. "A General Framework for Observation Driven Time-Varying Parameter Models," Tinbergen Institute Discussion Papers 08-108/4, Tinbergen Institute. [Downloadable!]
    Other versions:
  3. Ahoniemi, Katja & Lanne, Markku, 2007. "Joint Modeling of Call and Put Implied Volatility," MPRA Paper 6318, University Library of Munich, Germany. [Downloadable!]
    Other versions:
  4. 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 "G. Parenti". [Downloadable!]
  5. 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 "G. Parenti". [Downloadable!]
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