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Time Series Models in Non‐Normal Situations: Symmetric Innovations

Author

Listed:
  • M. L. Tiku
  • Wing‐Keung Wong
  • David C. Vaughan
  • Guorui Bian

Abstract

We consider AR(q) models in time series with non‐normal innovations represented by a member of a wide family of symmetric distributions (Student's t). Since the ML (maximum likelihood) estimators are intractable, we derive the MML (modified maximum likelihood) estimators of the parameters and show that they are remarkably efficient. We use these estimators for hypothesis testing, and show that the resulting tests are robust and powerful.

Suggested Citation

  • M. L. Tiku & Wing‐Keung Wong & David C. Vaughan & Guorui Bian, 2000. "Time Series Models in Non‐Normal Situations: Symmetric Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 571-596, September.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:5:p:571-596
    DOI: 10.1111/1467-9892.00199
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    Cited by:

    1. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    2. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    3. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    4. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    5. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    6. Abraão D. C. Nascimento & Maria C. S. Lima & Hassan Bakouch & Najla Qarmalah, 2023. "Scaled Muth–ARMA Process Applied to Finance Market," Mathematics, MDPI, vol. 11(8), pages 1-18, April.
    7. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.
    8. Yushan Cheng & Yongchang Hui & Michael McAleer & Wing-Keung Wong, 2021. "Spurious Relationships for Nearly Non-Stationary Series," JRFM, MDPI, vol. 14(8), pages 1-24, August.
    9. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    10. Eric S. Fung & Kin Lam & Tak-Kuen Siu & Wing-Keung Wong, 2011. "A Pseudo-Bayesian Model for Stock Returns In Financial Crises," JRFM, MDPI, vol. 4(1), pages 1-31, December.

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