A bootstrap test for threshold effects in a diffusion process

Heiko Rachinger, Edward M. H. Lin () and Henghsiu Tsai
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Heiko Rachinger: Universitat de les Illes Balears
Edward M. H. Lin: Tunghai University
Henghsiu Tsai: Institute of Statistical Science Academia Sinica

Computational Statistics, 2024, vol. 39, issue 5, No 18, 2859-2872

Abstract: 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.

Keywords: Bootstrap; Testing; Threshold diffusion process; Non-linear time series; Stochastic differential equation; Maximum likelihood estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01375-z

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