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|
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.:
- Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
- 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.).
- Diebold, Francis X., 1989. "Forecast combination and encompassing: Reconciling two divergent literatures," International Journal of Forecasting, Elsevier, vol. 5(4), pages 589-592.
- White,Halbert, 1994.
"Estimation, Inference and Specification Analysis,"
Cambridge University Press, number 9780521252805, October.
- 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.
- 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.
- 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.
- 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).
- 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.
- 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.
- Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
- Alexandra Dias & Paul Embrechts, 2004. "Dynamic copula models for multivariate high-frequency data in finance," Working Papers wpn04-01, Warwick Business School, Finance Group.
- 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.
- 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.
- Clements,Michael & Hendry,David, 1998.
"Forecasting Economic Time Series,"
Cambridge University Press, number 9780521634809, October.
- Timo Terasvirta & Clive W.J Granger & Andrew Patton, 2003.
"Common factors in conditional distributions for Bivariate time series,"
FMG Discussion Papers
dp455, Financial Markets Group.
- Granger, Clive W.J. & Terasvirta, Timo & Patton, Andrew J., 2006. "Common factors in conditional distributions for bivariate time series," Journal of Econometrics, Elsevier, vol. 132(1), pages 43-57, May.
- Kenneth D. West, 2000.
"Encompassing Tests When No Model Is Encompassing,"
NBER Technical Working Papers
0256, National Bureau of Economic Research, Inc.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:van:wpaper:0419. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (John P. Conley)
If references are entirely missing, you can add them using this form.