Computing the observed information in the hidden Markov model using the EM algorithm

1997 ◽  
Vol 32 (1) ◽  
pp. 107-114 ◽  
Author(s):  
James P. Hughes
Keyword(s):  
Markov Model ◽  
Em Algorithm ◽  
Hidden Markov Model ◽  
Hidden Markov ◽  
Observed Information ◽  
The Em Algorithm

scholarly journals Confidence Intervals for the Mixture Transition Distribution (MTD) Model and Other Markovian Models

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 351
Author(s):  
André Berchtold
Keyword(s):  
Markov Chains ◽  
Markov Model ◽  
Em Algorithm ◽  
Hidden Markov Model ◽  
Confidence Intervals ◽  
Hidden Markov ◽  
Simple Calculation ◽  
Standard Methods ◽  
Transition Distribution ◽  
Simulation Results

The Mixture Transition Distribution (MTD) model used for the approximation of high-order Markov chains does not allow a simple calculation of confidence intervals, and computationnally intensive methods based on bootstrap are generally used. We show here how standard methods can be extended to the MTD model as well as other models such as the Hidden Markov Model. Starting from existing methods used for multinomial distributions, we describe how the quantities required for their application can be obtained directly from the data or from one run of the E-step of an EM algorithm. Simulation results indicate that when the MTD model is estimated reliably, the resulting confidence intervals are comparable to those obtained from more demanding methods.

scholarly journals A Dependent Hidden Markov Model of Credit Quality

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Małgorzata Wiktoria Korolkiewicz
Keyword(s):  
Markov Chain ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Credit Rating ◽  
Hidden Markov ◽  
Credit Ratings ◽  
The State ◽  
Credit Quality ◽  
The Em Algorithm ◽  
Rating Process

We propose a dependent hidden Markov model of credit quality. We suppose that the "true" credit quality is not observed directly but only through noisy observations given by posted credit ratings. The model is formulated in discrete time with a Markov chain observed in martingale noise, where "noise" terms of the state and observation processes are possibly dependent. The model provides estimates for the state of the Markov chain governing the evolution of the credit rating process and the parameters of the model, where the latter are estimated using the EM algorithm. The dependent dynamics allow for the so-called "rating momentum" discussed in the credit literature and also provide a convenient test of independence between the state and observation dynamics.

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

2018 ◽  
Vol 35 (1-2) ◽  
pp. 51-72 ◽  
Author(s):  
Camilla Damian ◽  
Zehra Eksi ◽  
Rüdiger Frey
Keyword(s):  
Markov Model ◽  
Em Algorithm ◽  
Credit Risk ◽  
Hidden Markov Model ◽  
Point Process ◽  
Gaussian Noise ◽  
Goodness Of Fit ◽  
Markov Models ◽  
Hidden Markov ◽  
Process Observation

AbstractIn 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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