Semiparametric multivariate D-vine time series model
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This paper proposes a novel semiparametric multivariate D-vine time series model (mDvine) that enables the simultaneous copula-based modeling of both temporal and cross-sectional dependence for multivariate time series. To construct the mDvine, 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 the uDvine, we then construct the mDvine by joining multiple uDvines via another parametric copula. As a simple and tractable model, the mDvine provides flexible models for marginal behavior of time series and can also generate sophisticated temporal and cross-sectional dependence structures. Probabilistic properties of both the uDvine and mDvine are studied in detail. Furthermore, 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 the mDvine, and to examine the performance of the sequential model selection procedure and the two-stage MLE. Real data applications on the Australian electricity price and the Ireland wind speed data demonstrate the superior performance of the mDvine to traditional multivariate time series models.
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