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Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification. (English) Zbl 1418.62425

Summary: We introduce a new class of semiparametric copula-based multivariate dynamic (SCOMDY) models, which specify the conditional mean and the conditional variance of a multivariate time series parametrically, but specify the multivariate distribution of the standardized innovation semiparametrically as a parametric copula evaluated at nonparametric marginal distributions. We first study large sample properties of the estimators of SCOMDY model parameters under a misspecified parametric copula, then propose pseudo likelihood ratio (PLR) tests for model selection between two SCOMDY models with possibly misspecified copulas, and finally develop PLR tests for model selection between more than two SCOMDY models. The limiting null distributions of the PLR tests do not depend on the estimation of conditional mean and conditional variance parameters, hence are very easy to simulate. Empirical applications to three and higher dimensional daily exchange rate series indicate that a SCOMDY model with a tail-dependent copula is generally preferred.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H05 Characterization and structure theory for multivariate probability distributions; copulas
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[1] Breymann, W.; Dias, A.; Embrechts, P., Dependence structures for multivariate high-frequency data in finance, Quantitative finance, 3, 1, 1-16, (2003)
[2] Chen, X., Fan, Y., 2004. Asymptotic properties of several estimators for semiparametric copula-based multivariate dynamic models. Manuscript, New York University and Vanderbilt University.
[3] Chen, X., Fan, Y., 2005. Pseudo-likelihood ratio tests for model selection in semiparametric multivariate copula models. Canadian Journal of Statistics 33 (3), 389-414. · Zbl 1077.62032
[4] Chen, X., Fan, Y., Patton, A., 2003. Simple tests for models of dependence between multiple financial time series: with applications to US equity returns and exchange rates. Manuscript, New York University, Vanderbilt University and London School of Economics.
[5] Clements, M.; Hendry, D., Forecasting economic time series, (1998), Cambridge University Press Cambridge
[6] Corradi, V., Swanson, N., 2003. A test for comparing multiple misspecified conditional distributions. Manuscript, Rutgers University. · Zbl 1081.62011
[7] Corradi, V., Swanson, N., 2004. Predictive density accuracy tests. Manuscript, Rutgers University. · Zbl 1418.62438
[8] Dias, A., Embrechts, P., 2004. Dynamic copula models for multivariate high-frequency data in finance. Manuscript, ETH Zurich.
[9] Diebold, F., Forecast combination and encompassing: reconciling two divergent literature, International journal of forecasting, 5, 589-592, (1989)
[10] Diebold, F.; Hahn, J.; Tay, A., Multivariate density forecast evaluation and calibration in financial risk management: high frequency returns on foreign exchange, Review of economics and statistics, 81, 661-673, (1999)
[11] Elliott, G., Timmermann, A., 2002. Optimal forecast combinations under general loss functions and forecast error distributions. Manuscript, UCSD. · Zbl 1282.91266
[12] Engle, R., 2002. Dynamic conditional correlation—a simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20 (3), 339-350.
[13] Engle, R., McFadden, D., 1994. Handbook of Econometrics, vol. 4. Elsevier, New York. · Zbl 0982.62503
[14] Engle, R., Sheppard, K., 2001. Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH. Working paper, UCSD and New York University.
[15] Fermanian, J., 2003. Goodness of fit tests for copulas. Mimeo, CREST. · Zbl 1095.62052
[16] Genest, C.; Ghoudi, K.; Rivest, L., A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika, 82, 3, 543-552, (1995) · Zbl 0831.62030
[17] Giacomini, R., White, H., 2004. Tests of conditional predictive ability. Manuscript, UCSD. · Zbl 1187.91151
[18] Granger, C.W.J., 2002. Time series concept for conditional distributions. Manuscript, UCSD.
[19] Granger, C.W.J.; Teräsvirta, T., Modelling nonlinear economic relationships, (1993), Oxford University Press Oxford · Zbl 0893.90030
[20] Granger, C.W.J., Teräsvirta, T., Patton, A., 2003. Common factors in conditional distributions for bivariate time series. Journal of Econometrics, in press, doi:10.1016/j.jeconom.2005.01.022.
[21] Hamilton, J., Time series analysis, (1994), Princeton University Press Princeton
[22] Hansen, P., 2003. A test for superior predictive ability. Manuscript, Brown University.
[23] Hendry, D.; Richard, J., On the formulation of empirical models in dynamic econometrics, Journal of econometrics, 20, 3-33, (1982) · Zbl 0507.62096
[24] Hull, J.; White, A., Value at risk when daily changes in market variables are not normally distributed, Journal of derivatives, 5, 9-19, (1998)
[25] Joe, H., Multivariate models and dependence concepts, (1997), Chapman & Hall/CRC London · Zbl 0990.62517
[26] Junker, M., May, A., 2002. Measurement of Aggregate Risk With Copulas. Preprint, Caesar. · Zbl 1125.91351
[27] Machina, M., Granger, C., 2000. Forecast comparison without the use of cost functions. Working paper, UCSD.
[28] Marcellino, M., 2002. Model selection for nonlinear dynamic models. Manuscript.
[29] Mizon, G.; Richard, J., The encompassing principle and its application to testing non-nested hypotheses, Econometrica, 54, 657-678, (1986) · Zbl 0625.62105
[30] Nelsen, R., An introduction to copulas, (1999), Springer Berlin · Zbl 0909.62052
[31] Patton, A., 2002. Modeling time-varying exchange rate dependence using the conditional copula. Working Paper 01-09, University of California, San Diego.
[32] Patton, A., On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, Journal of financial econometrics, 2, 1, 130-168, (2004)
[33] Rivers, D., Vuong, Q., 2002. Model selection tests for nonlinear dynamic models. The Econometrics Journal 5 (1), 1-39. · Zbl 1010.62110
[34] Sin, C.; White, H., Information criteria for selecting possibly misspecified parametric models, Journal of econometrics, 71, 207-225, (1996) · Zbl 0843.62089
[35] Su, L., White, H., 2003. Multiple forecast comparison under general loss functions: \(\overline{\mathcal{X}}^2\) and resampling methods. Working paper, UCSD.
[36] Tsay, R., Analysis of financial time series, (2002), Wiley Interscience New York · Zbl 1037.91080
[37] Vuong, Q., Likelihood ratio test for model selection and non-nested hypotheses, Econometrica, 57, 307-333, (1989) · Zbl 0701.62106
[38] West, K., Encompassing tests when no model is encompassing, Journal of econometrics, 105, 287-308, (2001) · Zbl 1040.62110
[39] White, H., Estimation, inference and specification analysis, (1994), Cambridge University Press Cambridge, UK · Zbl 0860.62100
[40] White, H., A reality check for data snooping, Econometrica, 68, 1097-1126, (2000) · Zbl 1008.62116
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