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Contribution Details
| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Divide and Conquer: Recursive Likelihood Function Integration for Hidden Markov Models with Continuous Latent Variables |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Operations Research |
| Publisher | Institute for Operations Research and the Management Science |
| Geographical Reach | international |
| ISSN | 0030-364X |
| Volume | 66 |
| Number | 6 |
| Page Range | 1457 - 1759 |
| Date | 2018 |
| Abstract Text | This paper develops a method to efficiently estimate hidden Markov models with continuous latent variables using maximum likelihood estimation. To evaluate the (marginal) likelihood function, I decompose the integral over the unobserved state variables into a series of lower dimensional integrals, and recursively approximate them using numerical quadrature and interpolation. I show that this procedure has very favorable numerical properties: First, the computational complexity grows linearly in the number of periods, making the integration over hundreds and thousands of periods feasible. Second, I prove that the numerical error accumulates sublinearly in the number of time periods integrated, so the total error can be well controlled for a very large number of periods using, for example, Gaussian quadrature and Chebyshev polynomials. I apply this method to the bus engine replacement model of Rust [Econometrica 55(5): 999–1033] to verify the accuracy and speed of the procedure in both actual and simulated data sets. |
| Digital Object Identifier | 10.1287/opre.2018.1750 |
| Other Identification Number | merlin-id:17554 |
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