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A bootstrap test for threshold effects in a diffusion process

Author

Listed:
  • Heiko Rachinger

    (Universitat de les Illes Balears)

  • Edward M. H. Lin

    (Tunghai University)

  • Henghsiu Tsai

    (Institute of Statistical Science Academia Sinica)

Abstract

This paper proposes a bootstrap testing approach based on an approximate maximum likelihood method to discern whether a diffusion process is linear or whether there are threshold effects in the drift, the diffusion term or in both. It complements an alternative method based on the least-squares estimator which focuses on threshold effects in the drift. Monte Carlo simulations illustrate that the proposed testing approach is able to detect the source of the non-linearity. Two empirical applications show the importance of modeling threshold effects in the diffusion instead of the drift.

Suggested Citation

  • Heiko Rachinger & Edward M. H. Lin & Henghsiu Tsai, 2024. "A bootstrap test for threshold effects in a diffusion process," Computational Statistics, Springer, vol. 39(5), pages 2859-2872, July.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:5:d:10.1007_s00180-023-01375-z
    DOI: 10.1007/s00180-023-01375-z
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    References listed on IDEAS

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    1. Fei Su & Kung-Sik Chan, 2017. "Testing for Threshold Diffusion," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 218-227, April.
    2. Su, Fei & Chan, Kung-Sik, 2015. "Quasi-likelihood estimation of a threshold diffusion process," Journal of Econometrics, Elsevier, vol. 189(2), pages 473-484.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Yu, Ting-Hung & Tsai, Henghsiu & Rachinger, Heiko, 2020. "Approximate maximum likelihood estimation of a threshold diffusion process," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    5. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    6. Greta Goracci & Simone Giannerini & Kung-Sik Chan & Howell Tong, 2021. "Testing for threshold effects in the TARMA framework," Papers 2103.13977, arXiv.org.
    7. Fei Su & Kung-Sik Chan, 2016. "Option Pricing with Threshold Diffusion Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 133-141, April.
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