A Zero Serial Cross‐Correlation Test Before Fitting Heteroscedasticity
针对多元创新copula时间序列模型，提出在拟合多元异方差模型前检验异方差噪声的零序列互相关，用于判断使用单变量还是多变量GARCH模型，对汇率和共同基金收益的应用表明该检验必要。
ABSTRACT Many statistical inferences for a multivariate innovation‐based copula time series model rely on the serial independence of innovation vectors after filtering the conditional means and conditional covariance. Zero (respectively nonzero) serial cross‐correlations for the heteroscedastic noises before filtering the conditional covariance may suggest the use of univariate (respectively multivariate) GARCH models. This paper develops a zero serial cross‐correlation test for the heteroscedastic noises with heavy tails before fitting a multivariate heteroscedasticity model. Applications to exchange rates and mutual fund returns show that this critical assumption could be problematic sometimes and conducting such a test is necessary before building and using a multivariate innovation‐based copula time series model.