Publication Date: July 2020
Economic and ﬁnancial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We propose a procedure where nonstationarity is removed via a ﬁltration, and then the nonlinear temporal dependence in the ﬁltered data is captured via a flexible Markov copula. We study the asymptotic properties of two estimators of the parametric copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the ﬁltered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the ﬁltered series. We show that the limiting distribution of the parametric copula estimator depends on the nonstationary ﬁltration and the parametric marginal distribution estimation, and may be non-normal. Surprisingly, the limiting distribution of the semiparametric copula estimator using the ﬁltered data is shown to be the same as that without nonstationary ﬁltration, which is normal and free of marginal distribution speciﬁcation. The simple and robust properties of the semiparametric copula estimators extend to models with misspeciﬁed copulas, and facilitate statistical inferences, such as hypothesis testing and model selection tests, on semiparametric copula-based dynamic models in the presence of nonstationarity. Monte Carlo studies and real data applications are presented.
Keywords: Residual copula, Cointegration, Unit Root, Nonstationarity, Nonlinearity, Tail Dependence, Semiparametric
JEL Classification Codes: C14, C22