Modeling Multivariate Time Series with Copula-linked Univariate D-vines

TL;DR

This paper introduces CuDvine, a flexible copula-based multivariate time series model that captures both temporal and cross-sectional dependence, improving modeling accuracy for complex high-dimensional data.

Contribution

The paper develops CuDvine, a novel copula-linked univariate D-vine model that generalizes existing models and effectively captures complex dependence structures in multivariate time series.

Findings

CuDvine outperforms traditional models in real data applications.

The proposed estimation procedures are statistically robust and efficient.

Numerical experiments confirm the model's flexibility and effectiveness.

Abstract

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.