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On The Law Of Large Numbers For (Geometrically) Ergodic Markov Chains

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  • Jensen, S ren Tolver
  • Rahbek, Anders

Abstract

For use in asymptotic analysis of nonlinear time series models, we show that with (Xt,t 0) a (geometrically) ergodic Markov chain, the general version of the strong law of large numbers applies. That is, the average converges almost surely to the expectation of (Xt,Xt+1, ) irrespective of the choice of initial distribution of, or value of, X0. In the existing literature, the less general form has been studied.We thank Paolo Paruolo (the co-editor) and the referee for valuable comments. Also we thank the Danish Social Sciences Research Council (grant 2114-04-0001) for financial support.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 23 (2007)
Issue (Month): 04 (August)
Pages: 761-766

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Handle: RePEc:cup:etheor:v:23:y:2007:i:04:p:761-766_07

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Cited by:
  1. Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, School of Economics and Management, University of Aarhus.
  2. Konstantinos Fokianos & Anders Rahbek & Dag Tjøstheim, 2008. "Poisson Autoregression," Discussion Papers 08-35, University of Copenhagen. Department of Economics, revised Dec 2008.
  3. Line Elvstrøm Ekner & Emil Nejstgaard, 2013. "Parameter Identification in the Logistic STAR Model," Discussion Papers 13-07, University of Copenhagen. Department of Economics.
  4. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1719-1760, December.
  5. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
  6. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(6), pages 1205-1225, December.
  7. Peter Boswijk, H. & van der Weide, Roy, 2011. "Method of moments estimation of GO-GARCH models," Journal of Econometrics, Elsevier, vol. 163(1), pages 118-126, July.
  8. Anders Rahbek & Heino Bohn Nielsen, 2012. "Unit Root Vector Autoregression with volatility Induced Stationarity," CREATES Research Papers 2012-29, School of Economics and Management, University of Aarhus.
  9. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.

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