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Finite State Markov-Chain Approximations to Highly Persistent Processes

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  • Kopecky, Karen A.
  • Suen, Richard M. H.

Abstract

This paper re-examines the Rouwenhorst method of approximating first-order autoregressive processes. This method is appealing because it can match the conditional and unconditional mean, the conditional and unconditional variance and the first-order autocorrelation of any AR(1) process. This paper provides the first formal proof of this and other results. When comparing to five other methods, the Rouwenhorst method has the best performance in approximating the business cycle moments generated by the stochastic growth model. It is shown that, equipped with the Rouwenhorst method, an alternative approach to generating these moments has a higher degree of accuracy than the simulation method.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 15122.

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Date of creation: 08 May 2009
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Handle: RePEc:pra:mprapa:15122

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Keywords: Numerical Methods; Finite State Approximations; Optimal Growth Model;

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  1. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan Francisco Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  2. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 1-17, January.
  3. Karen A. Kopecky & Richard M. H. Suen, 2009. "Finite State Markov-Chain Approximations to Highly Persistent Processes," Working Papers 200904, University of California at Riverside, Department of Economics, revised May 2009.
  4. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  5. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
  6. Tauchen, George, 1990. "Solving the Stochastic Growth Model by Using Quadrature Methods and Value-Function Iterations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 49-51, January.
  7. Jerome Adda & Russell W. Cooper, 2003. "Dynamic Economics: Quantitative Methods and Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012014.
  8. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  9. Robert G. King & Sergio T. Rebelo, 2000. "Resuscitating Real Business Cycles," RCER Working Papers 467, University of Rochester - Center for Economic Research (RCER).
  10. Lkhagvasuren, Damba & Galindev, Ragchaasuren, 2008. "Discretization of highly persistent correlated AR(1) shocks," MPRA Paper 22523, University Library of Munich, Germany.
  11. Craig Burnside, 1998. "Discrete State-Space Methods for the Study of Dynamic Economies," QM&RBC Codes 125, Quantitative Macroeconomics & Real Business Cycles.
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  1. MC Approximations for ARs
    by Agent Continuum in Agent Continuum on 2010-06-20 02:17:57
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