Dynamic Copula-Based Markov Time Series

Abstract

Abstract This article examines a test procedure for checking the constancy of serial dependence via copulas for Markov time series data. It also provides a copula-based modeling approach for the dynamic serial dependence. Various parametric families of copulas offering different dependent structures are investigated. A score test is proposed for checking the constancy of a copula parameter. The score test is constructed and its asymptotic null distribution established under a two-stage estimation procedure. The test does not require specification of the probability distribution for the copula parameter. To capture the dynamics of dependence structure over time, autoregressive moving average and exponential type models are proposed. Illustrations are given based on simulated data and historic coffee prices data. Keywords: CopulaDynamic copulaKendall's tauMarkov time seriesScore testTime-varying parameterMathematics Subject Classification: Primary 62M02Secondary 62M10 Acknowledgment The work of Fentaw Abegaz was supported by a scholarship program from Addis Ababa University and MOE, Ethiopia and U.V. Naik-Nimbalkar's by CSIR, India. Notes Note: Values in parenthesis are estimates of Kendall measure of association. *Significant (p-value < 0.05).