Copula-based time series with filtered nonstationarity

Xiaohong Chen, Zhijie Xiao and Bo Wang

Journal of Econometrics, 2022, vol. 228, issue 1, 127-155

Abstract: 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 introduce 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 propose two estimators of the 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; Generated regressors; GNP and CAY residuals (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:228:y:2022:i:1:p:127-155

DOI: 10.1016/j.jeconom.2020.10.008

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