The Likelihood of Mixed Hitting Times

Jaap Abbring; Tim Salimans

The Likelihood of Mixed Hitting Times

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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 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 language	English
Place of Publication	Ithaca
Publisher	Cornell University Library
Number of pages	35
Publication status	Published - 9 May 2019

Publication series

Name	arXiv
Volume	1905.03463

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title = "The Likelihood of Mixed Hitting Times",

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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AU - Abbring, Jaap

AU - Salimans, Tim

PY - 2019/5/9

Y1 - 2019/5/9

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.

M3 - Discussion paper

T3 - arXiv

BT - The Likelihood of Mixed Hitting Times

PB - Cornell University Library

CY - Ithaca

ER -

The Likelihood of Mixed Hitting Times

Abstract

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