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Estimation, Model Diagnosis, and Process Control Under the Normal Model

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Copula-Based Markov Models for Time Series

Part of the book series: SpringerBriefs in Statistics ((JSSRES))

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Abstract

This chapter introduces statistical methods for copula-based Markov models under the normal margin. First, the data structures and the idea of statistical process control are reviewed. The copula-based Markov models and essential assumptions are introduced as well. Next, we derive the likelihood functions under the first-order and the second-order Markov models and define the maximum likelihood estimators (MLEs). We then give the asymptotic properties of the MLEs. We propose goodness-of-fit methods to test the model assumptions based on a given dataset. In addition, a copula model selection method is discussed. We introduce an R package Copula.Markov to implement the statistical methods of this chapter. Finally, we analyze three real datasets for illustration.

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Author information

Authors and Affiliations

  1. Graduate Institute of Statistics, National Central University, Taoyuan, Taiwan

    Li-Hsien Sun

  2. Institute of Statistics, National Chiao Tung University, Hsinchu, Taiwan

    Xin-Wei Huang

  3. Department of Mathematics, College of Sciences and Arts at Al Rass, Qassim University, Unayzah, Saudi Arabia

    Mohammed S. Alqawba

  4. Division of Science and Mathematics, University of Minnesota at Morris, Morris, MN, USA

    Jong-Min Kim

  5. Department of Information Management, Chang Gung University, Taoyuan, Taiwan

    Takeshi Emura

Authors
  1. Li-Hsien Sun
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  2. Xin-Wei Huang
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  3. Mohammed S. Alqawba
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  4. Jong-Min Kim
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  5. Takeshi Emura
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Corresponding author

Correspondence to Li-Hsien Sun .

Appendix: R Codes for Data Analysis

Appendix: R Codes for Data Analysis

The following R codes produce the results of our real data analysis in Sect. 3.7.

figure f

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Sun, LH., Huang, XW., Alqawba, M.S., Kim, JM., Emura, T. (2020). Estimation, Model Diagnosis, and Process Control Under the Normal Model. In: Copula-Based Markov Models for Time Series. SpringerBriefs in Statistics(). Springer, Singapore. https://doi.org/10.1007/978-981-15-4998-4_3

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