Copula-Based Markov Models for Time Series by Li-Hsien Sun & Xin-Wei Huang & Mohammed S. Alqawba & Jong-Min Kim & Takeshi Emura

Author:Li-Hsien Sun & Xin-Wei Huang & Mohammed S. Alqawba & Jong-Min Kim & Takeshi Emura
Language: eng
Format: epub
ISBN: 9789811549984
Publisher: Springer Singapore

The variance for is given by

Hence, the variance is decomposed into two parts: one is the squared difference between and , and the other is the weighted sum of and .

4.3 Parameter Estimation

This section proposes an estimation method under the proposed model in Sect. 4.2.

4.3.1 Maximum Likelihood Estimators

The log-likelihood function under the Clayton copula with the marginal normal mixture model is written as

where are observed data. The maximum likelihood estimator (MLE) is defined by

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