Computational methods for a copula-based markov chain model

• Main Author: Lee, Chin Yee
• Format: Final Year Project / Dissertation / Thesis
• Published: 2024
• Subjects: HA Statistics; QA Mathematics
• Online Access: http://eprints.utar.edu.my/6839/1/AM_2200494_Final_Lee_Chin_Yee.pdf; http://eprints.utar.edu.my/6839/

Copula-based Markov models have gained recognition as powerful tools for capturing intricate dependence structures in time series datasets. This study focuses on estimating parameters and assessing the performance of Clayton and Gaussian copulas in modelling Laplace distributed time series data. The Clayton and Gaussian copulas were chosen due to the Clayton copula’s capability to model tail dependencies and the Gaussian copula’s alignment with the data’s pseudo-observations. The ten-year daily log return of the SPX500 index is used in this study as the preliminary analysis revealed that it follows a Laplace distribution rather than the traditionally used t-distribution for modelling tail behaviour. Parameters were estimated using Maximum Likelihood Estimation (MLE) and the inversion of Kendall’s Tau, yielding feasible results for both copulas. The model’s performance was evaluated using the Root Mean Square Error (RMSE), with the Clayton copula achieving a lower RMSE of 0.01332 compared to 0.01541 for the Gaussian copula, indicating a better fit to the data. This study underscores the importance of selecting appropriate copulas, marginal distributions and estimation methods, demonstrating that the Clayton copula, combined with MLE, offers superior performance for modelling the Laplace distributed SPX500’s daily log returns.