Estimating the Error Distribution in the Multivariate Heteroscedastic Time Series Models
AbstractA semiparametric method is studied for estimating the dependence parameter and the joint distribution of the error term in a class of multivariate time series models when the marginal distributions of the errors are unknown. This method is a natural extension of Genest et al. (1995a) for independent and identically distributed observations. The proposed method first obtains √n-consistent estimates of the parameters of each univariate marginal time-series, and computes the corresponding residuals. These are then used to estimate the joint distribution of the multivariate error terms, which is specified using a copula. Our developments and proofs make use of, and build upon, recent elegant results of Koul and Ling (2006) and Koul (2002) for these models. The rigorous proofs provided here also lay the foundation and collect together the technical arguments that would be useful for other potential extensions of this semiparametric approach. It is shown that the proposed estimator of the dependence parameter of the multivariate error term is asymptotically normal, and a consistent estimator of its large sample variance is also given so that confidence intervals may be constructed. A large scale simulation study was carried out to compare the estimators particularly when the error distributions are unknown, which is almost always the case in practice. In this simulation study, our proposed semiparametric method performed better than the well-known parametric methods. An example on exchange rates is used to illustrate the method.
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Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 8/07.
Length: 27 pages
Date of creation: Jun 2007
Date of revision:
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Web page: http://www.buseco.monash.edu.au/depts/ebs/
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Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-06-23 (All new papers)
- NEP-ECM-2007-06-23 (Econometrics)
- NEP-ETS-2007-06-23 (Econometric Time Series)
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