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.
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The author thanks the referee for useful comments on an earlier draft of this article.
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Weiß, C.H. On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains. Methodol Comput Appl Probab 19, 997–1007 (2017). https://doi.org/10.1007/s11009-017-9560-9
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DOI: https://doi.org/10.1007/s11009-017-9560-9