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.
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Acknowledgements
We would like to express our gratitude to the Co-Editor and the four reviewers for their valuable comments, which led to a substantial improvement of the paper. Henghsiu Tsai’s research was supported by Academia Sinica, the Mathematics Research Promotion Center, and Ministry of Science and Technology of the Republic of China under grant number MOST 108-2118-M-001-003-MY2 and MOST 110-2118-M-001-004-MY2. Edward M.H. Lin’s research is supported by the Ministry of Science and Technology of the Republic of China under grant number MOST 110-2118-M-029-001, and MOST 111-2118-M-029 -003 -MY2. Part of this paper was written while Heiko Rachinger was visiting Academia Sinica.
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Rachinger, H., Lin, E.M.H. & Tsai, H. A bootstrap test for threshold effects in a diffusion process. Comput Stat (2023). https://doi.org/10.1007/s00180-023-01375-z
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DOI: https://doi.org/10.1007/s00180-023-01375-z