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

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  • Christian H. Weiß

    (Helmut Schmidt University)

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.

Suggested Citation

  • Christian H. Weiß, 2017. "On Eigenvalues of the Transition Matrix of Some Count-Data Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 997-1007, September.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:3:d:10.1007_s11009-017-9560-9
    DOI: 10.1007/s11009-017-9560-9
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    References listed on IDEAS

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    3. Christian H. Weiß & Hee‐Young Kim, 2014. "Diagnosing and modeling extra‐binomial variation for time‐dependent counts," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(5), pages 588-608, September.
    4. Christian H. Weiß & Philip K. Pollett, 2014. "Binomial Autoregressive Processes With Density-Dependent Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 115-132, March.
    5. HEINEN, Andréas, 2003. "Modelling time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003062, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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