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Multiplicative Error Models

Financial time series analysis has focused on data related to market trading activity. Next to the modeling of the conditional variance of returns within the GARCH family of models, recent attention has been devoted to other variables: first, and foremost, volatility measured on the basis of ultra-high frequency data, but also volumes, number of trades, durations. In this paper, we examine a class of models, named Multiplicative Error Models, which are particularly suited to model such non-negative time series. We discuss the univariate specification, by considering the base choices for the conditional expectation and the error term. We provide also a general framework, allowing for richer specifications of the conditional mean. The outcome is a novel MEM (called Composite MEM) which is reminiscent of the short- and long-run component GARCH model by Engle and Lee (1999). Inference issues are discussed relative to Maximum Likelihood and Generalized Method of Moments estimation. In the application, we show the regularity in parameter estimates and forecasting performance obtainable by applying the MEM to the realized kernel volatility of components of the S&P100 index. We suggest extensions of the base model by enlarging the information set and adopting a multivariate specification.

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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 2011_03.

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Length: 26 pages
Date of creation: Feb 2011
Date of revision: Apr 2011
Publication status: Forthcoming in 'Volatility Models and Their Applications' (Luc Bauwens, Christian Hafner, Sebastien Laurent eds.)
Handle: RePEc:fir:econom:wp2011_03
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  1. Ahoniemi, Katja & Lanne, Markku, 2007. "Joint Modeling of Call and Put Implied Volatility," MPRA Paper 6318, University Library of Munich, Germany.
  2. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836, May.
  3. 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.
  4. BAUWENS, Luc & ROMBOUTS, Jeroen, 2003. "Bayesian clustering of many GARCH models," CORE Discussion Papers 2003087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Neil Shephard & Kevin Sheppard, 2009. "Realising the future: forecasting with high frequency based volatility (HEAVY) models," Economics Papers 2009-W03, Economics Group, Nuffield College, University of Oxford.
  6. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
  7. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  8. Cavit Pakel & Neil Shephard & Kevin Sheppard, 2009. "Nuisance parameters, composite likelihoods and a panel of GARCH models," OFRC Working Papers Series 2009fe03, Oxford Financial Research Centre.
  9. 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.
  10. Pierre Giot & Sébastien Laurent, 2002. "Modelling Daily Value-at-Risk Using Realized Volatility and ARCH Type Models," Computing in Economics and Finance 2002 52, Society for Computational Economics.
  11. 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.
  12. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2010. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series 2010/19, Center for Financial Studies (CFS).
  13. Christian FRANCQ & Lajos HORVATH & Jean-Michel ZAKOIAN, 2009. "Merits and Drawbacks of Variance Targeting in GARCH Models," Working Papers 2009-17, Centre de Recherche en Economie et Statistique.
  14. 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.
  15. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  16. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
  17. 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.
  18. Christian T. Brownlees & Giampiero Gallo, 2006. "Financial Econometric Analysis at Ultra–High Frequency: Data Handling Concerns," Econometrics Working Papers Archive wp2006_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  19. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Intra-daily Volume Modeling and Prediction for Algorithmic Trading," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(3), pages 489-518, Summer.
  20. Kristensen, Dennis & Linton, Oliver, 2004. "03.5.2. Consistent Standard Errors for Target Variance Approach to GARCH Estimation Solution," Econometric Theory, Cambridge University Press, vol. 20(05), pages 990-993, October.
  21. Markku Lanne, 2006. "A Mixture Multiplicative Error Model for Realized Volatility," Economics Working Papers ECO2006/3, European University Institute.
  22. 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.
  23. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  24. Manganelli, Simone, 2002. "Duration, volume and volatility impact of trades," Working Paper Series 0125, European Central Bank.
  25. 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.
  26. Robert F. Engle & Giampiero M. Gallo & Margherita Velucchi, 2012. "Volatility Spillovers in East Asian Financial Markets: A Mem-Based Approach," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 222-223, February.
  27. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages C1-C32, November.
  28. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  29. 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.
  30. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
  31. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  32. 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".
  33. Peter Reinhard Hansen & Zhuo (Albert) Huang & Howard Howan Shek, . "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.
  34. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
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