# Estimating the error distribution in multivariate regression and time series models

#### by Mervyn Silvapulle

Institution: Department of Econometrics and Business Statistics, Monash University
Date: Tue 3rd June 2008
Time: 1:15 PM
Location: Room 213 Richard Berry Bldg, The University of Melbourne

Abstract: Copulas have attracted considerable interest for modelling multivariate
observations. In this paper, a semiparametric method is studied for
estimating the copula parameter and the joint distribution of the error
term in a class of multivariate regression and GARCH-type time series
models when the marginal distributions of the errors are unknown. This
method is a direct extension of that proposed by Genest, Rivest, Ghoudi
(1995, Biometrika). The method first obtains $\sqrt{n}$-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. The proposed estimator of the copula
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 simulation study was carried
out to compare the estimators particularly when the error distributions
are unknown. In this simulation study, the proposed semiparametric method
performed better than the other competing parametric methods. An example
on exchange rates is used to illustrate the method.