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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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    1. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    2. Tina Hviid Rydberg & Neil Shephard, 2000. "BIN Models for Trade-by-Trade Data. Modelling the Number of Trades in a Fixed Interval of Time," Econometric Society World Congress 2000 Contributed Papers 0740, Econometric Society.
    3. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    4. HEINEN, Andreas & RENGIFO, Erick, 2003. "Multivariate modelling of time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. 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.
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