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


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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.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Statistics and Risk Modeling
WU-Journal-Rating new FIN-A, VW-C
Language English
Title EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies
Volume 35
Number 1-2
Year 2018
Page from 51
Page to 72
Reviewed? Y
DOI http://dx.doi.org/10.1515/strm-2017-0021
Open Access N

Associations

People
Damian, Camilla (Details)
Eksi-Altay, Zehra (Details)
Frey, Rüdiger (Details)
Organization
Institute for Statistics and Mathematics IN (Details)
Research areas (ÖSTAT Classification 'Statistik Austria')
1118 Probability theory (Details)
1137 Financial mathematics (Details)
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