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EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies

Damian, Camilla and Eksi-Altay, Zehra and Frey, Rüdiger (2018) EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies. Statistics and Risk Modeling, 35 (1-2). pp. 51-72. ISSN 2196-7040

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Abstract

In this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

Item Type: Article
Additional Information: Camilla Damian and Rüdiger Frey are grateful for the support by the Vienna Science and Technology Fund (WWTF) through project MA14-031.
Keywords: Expectation maximization (EM) algorithm, hidden Markov models, point processes, nonlinear filtering, goodness-of-fit tests, credit risk ratings
Classification Codes: MSC 2010: 60G35; 62P05
Divisions: Departments > Finance, Accounting and Statistics > Statistics and Mathematics
Version of the Document: Published
Depositing User: Gertraud Novotny
Date Deposited: 08 May 2019 11:43
Last Modified: 08 May 2019 11:44
Related URLs:
FIDES Link: https://bach.wu.ac.at/d/research/results/84767/
URI: http://epub.wu.ac.at/id/eprint/6952

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