Estimation under copula-based Markov normal mixture models for serially correlated data

Abstract

We propose an estimation method under a copula-based Markov model for serially correlated data. Motivated by the fat-tailed distribution of financial assets, we select a normal mixture distribution for the marginal distribution. Based on the normal mixture distribution for the marginal distribution and the Clayton copula for serial dependence, we obtain the corresponding likelihood function. In order to obtain the maximum likelihood estimators, we apply the Newton-Raphson algorithm with appropriate transformations and initial values. We conduct simulation studies to evaluate the performance of the proposed method. In the empirical analysis, the stock price of Dow Jones Industrial Average is analyzed for illustration.

Keywords:

• Log return
• Copula
• Normal mixture distribution
• Newton-Raphson algorithm
• Markov model

Acknowledgments

The authors would like to thank anonymous reviewers for the comments to improve the presentation of this paper.

Additional information

Funding

The project is supported by the Ministry of Science and Technology of the Republic of China (MOST) grant 105-2118-M-008-005 and MOST grant 106-2118-M-008-001.