The Likelihood of Mixed Hitting Times

Jaap Abbring, Tim Salimans

Research output: Working paperDiscussion paperOther research output

Abstract

We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of Lévy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.
Original languageEnglish
Place of PublicationIthaca
PublisherCornell University Library
Number of pages35
Publication statusPublished - 9 May 2019

Publication series

NamearXiv
Volume1905.03463

Fingerprint

Hitting Time
Laplace transform
Likelihood
Latent Process
First Passage Time
Maximum Likelihood Estimator
MATLAB
Closed-form
Numerical Methods
Estimator
Computing
Model

Cite this

Abbring, J., & Salimans, T. (2019). The Likelihood of Mixed Hitting Times. (arXiv; Vol. 1905.03463). Ithaca: Cornell University Library.
Abbring, Jaap ; Salimans, Tim. / The Likelihood of Mixed Hitting Times. Ithaca : Cornell University Library, 2019. (arXiv).
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abstract = "We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent L{\'e}vy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of L{\'e}vy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.",
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Abbring, J & Salimans, T 2019 'The Likelihood of Mixed Hitting Times' arXiv, vol. 1905.03463, Cornell University Library, Ithaca.

The Likelihood of Mixed Hitting Times. / Abbring, Jaap; Salimans, Tim.

Ithaca : Cornell University Library, 2019. (arXiv; Vol. 1905.03463).

Research output: Working paperDiscussion paperOther research output

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T1 - The Likelihood of Mixed Hitting Times

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AU - Salimans, Tim

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N2 - We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of Lévy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.

AB - We present a method for computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of Lévy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan's (1985) strike data.

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Abbring J, Salimans T. The Likelihood of Mixed Hitting Times. Ithaca: Cornell University Library. 2019 May 9. (arXiv).