On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains

On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains We analyze the eigenstructure of count-data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Statistics; Statistics, general; Life Sciences, general; Electrical Engineering; Economics, general; Business and Management, general
ISSN
1387-5841
eISSN
1573-7713
D.O.I.
10.1007/s11009-017-9560-9
Publisher site
See Article on Publisher Site

Abstract

We analyze the eigenstructure of count-data Markov chains. Our main focus is on so-called CLAR(1) models, which are characterized by having a linear conditional mean, and also on the case of a finite range, where the second largest eigenvalue determines the speed of convergence of the forecasting distributions. We derive a lower bound for the second largest eigenvalue, which often (but not always) even equals this eigenvalue. This becomes clear by deriving the complete set of eigenvalues for several specific cases of CLAR(1) models.

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Mar 31, 2017

References

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