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An evolutionary algorithm for the estimation of threshold vector error correction models

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  • Makram El-Shagi

Abstract

We develop an evolutionary algorithm to estimate Threshold Vector Error Correction models (TVECM) with more than two cointegrated variables. Since disregarding a threshold in cointegration models renders standard approaches to the estimation of the cointegration vectors inefficient, TVECM necessitate a simultaneous estimation of the cointegration vector(s) and the threshold. As far as two cointegrated variables are considered this is commonly achieved by a grid search. However, grid search quickly becomes computationally unfeasible if more than two variables are cointegrated. Therefore, the likelihood function has to be maximized using heuristic approaches. Depending on the precise problem structure the evolutionary approach developed in the present paper for this purpose saves 90 to 99 per cent of the computation time of a grid search.
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  • Makram El-Shagi, 2011. "An evolutionary algorithm for the estimation of threshold vector error correction models," International Economics and Economic Policy, Springer, vol. 8(4), pages 341-362, December.
    • Handle: RePEc:kap:iecepo:v:8:y:2011:i:4:p:341-362
    DOI: 10.1007/s10368-011-0180-5
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    1. Yang, Zheng & Tian, Zheng & Yuan, Zixia, 2007. "GSA-based maximum likelihood estimation for threshold vector error correction model," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 109-120, September.
    2. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    3. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    4. Baragona, R. & Battaglia, F. & Cucina, D., 2004. "Fitting piecewise linear threshold autoregressive models by means of genetic algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 277-295, September.
    5. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    6. Winker, Peter & Gilli, Manfred, 2004. "Applications of optimization heuristics to estimation and modelling problems," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 211-223, September.
    7. Qu, Zhongjun & Perron, Pierre, 2007. "A Modified Information Criterion For Cointegration Tests Based On A Var Approximation," Econometric Theory, Cambridge University Press, vol. 23(4), pages 638-685, August.
    8. Jamie Gascoigne, 2004. "Estimating threshold vector error-correction models with multiple cointegrating relationships," Working Papers 2004013, The University of Sheffield, Department of Economics, revised Nov 2004.
    9. Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
    10. Gonzalo, Jesùs & Pitarakis, Jean-Yves, 2005. "Threshold effects In multivariate error correction models," Discussion Paper Series In Economics And Econometrics 0501, Economics Division, School of Social Sciences, University of Southampton.
    11. Doherr, Thorsten & Czarnitzki, Dirk, 2002. "Genetic algorithms: a tool for optimization in econometrics - basic concept and an example for empirical applications," ZEW Discussion Papers 02-41, ZEW - Leibniz Centre for European Economic Research.
    12. Dorsey, Robert E & Mayer, Walter J, 1995. "Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 53-66, January.
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    Cited by:

    1. Schleer, Frauke, 2013. "Finding starting-values for maximum likelihood estimation of vector STAR models," ZEW Discussion Papers 13-076, ZEW - Leibniz Centre for European Economic Research.
    2. Frauke Schleer, 2015. "Finding Starting-Values for the Estimation of Vector STAR Models," Econometrics, MDPI, vol. 3(1), pages 1-26, January.
    3. El-Shagi, Makram, 2017. "Dealing with small sample bias in post-crisis samples," Economic Modelling, Elsevier, vol. 65(C), pages 1-8.
    4. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.
    5. El-Shagi, Makram & Giesen, Sebastian, 2010. "Money and Inflation: The Role of Persistent Velocity Movements," IWH Discussion Papers 2/2010, Halle Institute for Economic Research (IWH).

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    More about this item

    Keywords

    Threshold cointegration; Evolutionary algorithms; Genetic algorithms; Evolutionary strategies; C61; C32;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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