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Markov-chain approximations of vector autoregressions: application of general multivariate-normal integration techniques

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  • Edward S. Knotek
  • Stephen J. Terry

Abstract

Discrete Markov chains can be useful to approximate vector autoregressive processes for economists doing computational work. One such approximation method first presented by Tauchen (1986) operates under the general theoretical assumption of a transformed VAR with diagonal covariance structure for the process error term. We demonstrate one simple method of more conveniently treating this approximation problem in practice using readily available multivariate-normal integration techniques to allow for arbitrary positive-semidefinite covariance structures. Examples are provided using processes with non-diagonal and singular non-diagonal error covariances.

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  • Edward S. Knotek & Stephen J. Terry, 2008. "Markov-chain approximations of vector autoregressions: application of general multivariate-normal integration techniques," Research Working Paper RWP 08-02, Federal Reserve Bank of Kansas City.
  • Handle: RePEc:fip:fedkrw:rwp08-02
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    1. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-396, March.
    2. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
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    Cited by:

    1. Leland E. Farmer & Alexis Akira Toda, 2017. "Discretizing nonlinear, non‐Gaussian Markov processes with exact conditional moments," Quantitative Economics, Econometric Society, vol. 8(2), pages 651-683, July.
    2. Di Nicolo, G. & Gamba, A. & Lucchetta, M., 2011. "Capital Regulation, Liquidity Requirements and Taxation in a Dynamic Model of Banking," Other publications TiSEM 58ac9f00-92d7-497b-a76f-e, Tilburg University, School of Economics and Management.
    3. Groneck, Max & Wallenius, Johanna, 2017. "It Sucks to Be Single! Marital Status and Redistribution of Social Security," SSE Working Paper Series in Economics 2017:1, Stockholm School of Economics.
    4. Carlos Hatchondo, Juan & Martinez, Leonardo & Sánchez, Juan M., 2015. "Mortgage defaults," Journal of Monetary Economics, Elsevier, vol. 76(C), pages 173-190.
    5. Galindev, Ragchaasuren & Lkhagvasuren, Damba, 2010. "Discretization of highly persistent correlated AR(1) shocks," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1260-1276, July.
    6. Gospodinov, Nikolay & Lkhagvasuren, Damba, 2011. "A new method for approximating vector autoregressive processes by finite-state Markov chains," MPRA Paper 33827, University Library of Munich, Germany.
    7. Reyes-Heroles, Ricardo & Tenorio, Gabriel, 2020. "Macroprudential policy in the presence of external risks," Journal of International Economics, Elsevier, vol. 126(C).
    8. Mitsuru Katagiri, 2018. "Equilibrium Yield Curve, the Phillips Curve, and Monetary Policy," IMF Working Papers 18/242, International Monetary Fund.
    9. Nikolay Gospodinov & Damba Lkhagvasuren, 2014. "A Moment‐Matching Method For Approximating Vector Autoregressive Processes By Finite‐State Markov Chains," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 843-859, August.
    10. Di Nicolo, G. & Gamba, A. & Lucchetta, M., 2011. "Capital Regulation, Liquidity Requirements and Taxation in a Dynamic Model of Banking," Discussion Paper 2011-090, Tilburg University, Center for Economic Research.
    11. Gete, Pedro & Porchia, Paolo, 2010. "Fertility and Consumption when Having a Child is a Risky Investment," MPRA Paper 27885, University Library of Munich, Germany.
    12. Samer Shousha, 2017. "International Reserves, Credit Constraints, and Systemic Sudden Stops," International Finance Discussion Papers 1205, Board of Governors of the Federal Reserve System (U.S.).
    13. Sergio J. Rey & Wei Kang & Levi Wolf, 2016. "The properties of tests for spatial effects in discrete Markov chain models of regional income distribution dynamics," Journal of Geographical Systems, Springer, vol. 18(4), pages 377-398, October.
    14. Andrea Gamba & Alexander J. Triantis, 2014. "Corporate Risk Management: Integrating Liquidity, Hedging, and Operating Policies," Management Science, INFORMS, vol. 60(1), pages 246-264, January.
    15. Edward S. Knotek & Stephen J. Terry, 2008. "Alternative methods of solving state-dependent pricing models," Research Working Paper RWP 08-10, Federal Reserve Bank of Kansas City.

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