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. In the empirical analysis, the stock price of Dow Jones Industrial Average is analyzed for illustration.
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4.1 Electronic supplementary material
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Appendix: R codes
Appendix: R codes
Below are the R codes for implementing the data analysis.
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library(Copula.Markov)
data(DowJones)
Y=as.vector(DowJones$\(\mathrm {log\_return}\))
Clayton.MixNormal.Markov.MLE(y=Y)
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Sun, LH., Huang, XW., Alqawba, M.S., Kim, JM., Emura, T. (2020). Estimation Under Normal Mixture Models for Financial Time Series Data. In: Copula-Based Markov Models for Time Series. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-4998-4_4
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DOI: https://doi.org/10.1007/978-981-15-4998-4_4
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