Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification
Recently Chen and Fan (2003a) introduced a new class of semiparametric copula-based multivariate dynamic (SCOMDY) models. A SCOMDY model specifies the conditional mean and the conditional variance of a multivariate time series parametrically (such as VAR, GARCH), but specifies the multivariate distribution of the standardized innovation semiparametrically as aparametric copula evaluated at nonparametric marginal distributions. In this paper, we first study large sample properties of the estimators of SCOMDY model parameters under a misspecified parametric copula, and then establish pseudo likelihood ratio (PLR) tests for model selection between two SCOMDY models with possibly misspecified copulas. Finally we develop PLR tests for model selection between more than two SCOMDY models along the lines of the reality check of White (2000). The limiting distributions of the estimators of copula parameters and the PLR tests do not depend on the estimation of conditional mean and conditional variance parameters. Although the tests are affected by the estimation of unknown marginal distributions of standardized innovations, they have standard parametric rates and the limiting null distributions are very easy to simulate. Empirical applications to multiple daily exchange rate data indicate the simplicity and usefulness of the proposed tests. Although a SCOMDY model with Gaussian copula might be a reasonable model for some bivariate FX series, but a SCOMDY model with a copula which has (asymmetric) tail-dependence is generally preferred for tri-variate and higher dimensional FX series.
|Date of creation:||Feb 2004|
|Date of revision:||Sep 2004|
|Contact details of provider:|| Web page: http://www.vanderbilt.edu/econ/wparchive/index.html|
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- Elliott, Graham & Timmermann, Allan, 2002.
"Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions,"
University of California at San Diego, Economics Working Paper Series
qt15r9t2q2, Department of Economics, UC San Diego.
- Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
- repec:cup:cbooks:9780521634809 is not listed on IDEAS
- Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
- Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
- Granger, Clive W.J. & TerÃ¤svirta, Timo & Patton, Andrew J, 2002.
"Common Factors in Conditional Distributions,"
University of California at San Diego, Economics Working Paper Series
qt3bd1n1x5, Department of Economics, UC San Diego.
- Granger, Clive W.J. & Teräsvirta, Timo & Patton, Andrew J., 2002. "Common factors in conditional distributions," SSE/EFI Working Paper Series in Economics and Finance 515, Stockholm School of Economics.
- Clive W. J. Granger, 2003. "Time Series Concepts for Conditional Distributions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 689-701, December.
- Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
- Massimiliano Marcellino, . "Model Selection for Non-Linear Dynamic Models," Working Papers 159, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
- West,K.D., 1999.
"Encompassing tests when no model is encompassing,"
36, Wisconsin Madison - Social Systems.
- W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
- Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
- Andrew J. Patton, 2004.
"On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation,"
Journal of Financial Econometrics,
Society for Financial Econometrics, vol. 2(1), pages 130-168.
- Andrew J. Patton, 2002. "On the out-of-sample importance of skewness and asymetric dependence for asset allocation," LSE Research Online Documents on Economics 24951, London School of Economics and Political Science, LSE Library.
- Jean-David Fermanian, 2003. "Goodness of Fit Tests for Copulas," Working Papers 2003-34, Centre de Recherche en Economie et Statistique.
- Hendry, David F. & Richard, Jean-Francois, 1982.
"On the formulation of empirical models in dynamic econometrics,"
Journal of Econometrics,
Elsevier, vol. 20(1), pages 3-33, October.
- HENRY, David F. & RICHARD, Jean-François, . "On the formulation of empirical models in dynamic econometrics," CORE Discussion Papers RP -502, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Alexandra Dias & Paul Embrechts, 2004. "Dynamic copula models for multivariate high-frequency data in finance," Working Papers wpn04-01, Warwick Business School, Finance Group.
- Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics.
- Robert F. Engle & Kevin Sheppard, 2001.
"Theoretical and Empirical properties of Dynamic Conditional Correlation Multivariate GARCH,"
NBER Working Papers
8554, National Bureau of Economic Research, Inc.
- Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
- Norman Swanson & Valentina Corradi, 2004. "Predictive Density Accuracy Tests," Working Papers wp04-16, Warwick Business School, Finance Group.
- Raffaella Giacomini & Halbert White, 2006.
"Tests of Conditional Predictive Ability,"
Econometric Society, vol. 74(6), pages 1545-1578, November.
- Giacomini, Raffaella & White, Halbert, 2003. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series qt5jk0j5jh, Department of Economics, UC San Diego.
- Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
- Raffaella Giacomini & Halbert White, 2003. "Tests of Conditional Predictive Ability," Econometrics 0308001, EconWPA.
- Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
- Diebold, Francis X., 1989.
"Forecast combination and encompassing: Reconciling two divergent literatures,"
International Journal of Forecasting,
Elsevier, vol. 5(4), pages 589-592.
- Francis X. Diebold, 1989. "Forecast combination and encompassing: reconciling two divergent literatures," Finance and Economics Discussion Series 80, Board of Governors of the Federal Reserve System (U.S.).
- Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
- White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
- Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group.
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