# The Likelihood of Mixed Hitting Times

## TL;DR

This paper introduces a numerical method to compute the likelihood of mixed hitting-time models involving Lévy processes, enabling maximum likelihood estimation and application to strike data analysis.

## Contribution

The paper develops a novel numerical approach for inverting Laplace transforms to compute likelihoods in mixed hitting-time models involving Lévy processes.

## Key findings

- Successfully implemented maximum likelihood estimator in MATLAB.
- Applied the method to analyze Kennan's strike data.
- Demonstrated the method's effectiveness in real-world data analysis.

## 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\'evy 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\'evy 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.