  This paper proposes a novel multivariate time series model named
Copula-linked univariate D-vines (CuDvine), which enables the simultaneous
copula-based modeling of both temporal and cross-sectional dependence for
multivariate time series. To construct CuDvine, we first build a semiparametric
univariate D-vine time series model (uDvine) based on a D-vine. The uDvine
generalizes the existing first-order copula-based Markov chain models to Markov
chains of an arbitrary-order. Building upon uDvine, we construct CuDvine by
linking multiple uDvines via a parametric copula. As a simple and tractable
model, CuDvine provides flexible models for marginal behavior and temporal
dependence of time series, and can also incorporate sophisticated
cross-sectional dependence such as time-varying and spatio-temporal dependence
for high-dimensional applications. Robust and computationally efficient
procedures, including a sequential model selection method and a two-stage MLE,
are proposed for model estimation and inference, and their statistical
properties are investigated. Numerical experiments are conducted to demonstrate
the flexibility of CuDvine, and to examine the performance of the sequential
model selection procedure and the two-stage MLE. Real data applications on the
Australian electricity price data demonstrate the superior performance of
CuDvine to traditional multivariate time series models.
