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Numerical issues in threshold autoregressive modeling of time series

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  • Coakley, Jerry
  • Fuertes, Ana-Maria
  • Perez, Maria-Teresa

Abstract

This paper analyses the contribution of various numerical approaches to making the estimation of threshold autoregressive time series more efficient. It relies on the computational advantages of QR factorizations and proposes Givens transformations to update these factors for sequential LS problems. By showing that the residual sum of squares is a continuous rational function over threshold intervals it develops a new fitting method based on rational interpolation and the standard necessary optimality condition. Taking as benchmark a simple grid search, the paper illustrates via Monte Carlo simulations the efficiency gains of the proposed tools.
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Suggested Citation

  • Coakley, Jerry & Fuertes, Ana-Maria & Perez, Maria-Teresa, 2003. "Numerical issues in threshold autoregressive modeling of time series," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2219-2242, September.
  • Handle: RePEc:eee:dyncon:v:27:y:2003:i:11-12:p:2219-2242
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    References listed on IDEAS

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    1. 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.
    2. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
    3. Pesaran, M. Hashem & Potter, Simon M., 1997. "A floor and ceiling model of US output," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 661-695, May.
    4. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    5. Kapetanios, G., 1999. "Model Selection in Threshold Models," Cambridge Working Papers in Economics 9906, Faculty of Economics, University of Cambridge.
    6. Coakley, Jerry & Fuertes, Ana-Maria, 2001. "A Non-linear Analysis of Excess Foreign Exchange Returns," Manchester School, University of Manchester, vol. 69(6), pages 623-642, December.
    7. Coakley, Jerry & Fuertes, Ana-Maria, 2001. "Border costs and real exchange rate dynamics in Europe," Journal of Policy Modeling, Elsevier, vol. 23(6), pages 669-676, August.
    8. Philip Rothman, 1999. "Time Series Evidence on Whether Adjustment to Long-Run Equilibrium is Asymmetric," Working Papers 9904, East Carolina University, Department of Economics.
    9. Kapetanios, G., 1999. "Threshold Models for Trended Time Series," Cambridge Working Papers in Economics 9905, Faculty of Economics, University of Cambridge.
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    Citations

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    Cited by:

    1. Norman, Stephen, 2008. "Systematic small sample bias in two regime SETAR model estimation," Economics Letters, Elsevier, vol. 99(1), pages 134-138, April.
    2. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Valuation ratios and price deviations from fundamentals," Journal of Banking & Finance, Elsevier, vol. 30(8), pages 2325-2346, August.
    3. Gilles Dufrenot & Dominique Guegan & Anne Peguin-Feissolle, 2008. "Changing-regime volatility: a fractionally integrated SETAR model," Applied Financial Economics, Taylor & Francis Journals, vol. 18(7), pages 519-526.
    4. Laurent Ferrara & Dominique Guégan, 2006. "Detection of the Industrial Business Cycle using SETAR Models," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2005(3), pages 353-371.
    5. Dufrenot, Gilles & Guegan, Dominique & Peguin-Feissolle, Anne, 2005. "Long-memory dynamics in a SETAR model - applications to stock markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(5), pages 391-406, December.
    6. Chen, An-Sing & Lin, Shih-Chieh, 2011. "Asymmetrical return on equity mean reversion and catering," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 471-477, February.
    7. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    8. Marian Vavra, 2012. "A Note on the Finite Sample Properties of the CLS Method of TAR Models," Birkbeck Working Papers in Economics and Finance 1206, Birkbeck, Department of Economics, Mathematics & Statistics.
    9. Mark P. Taylor, 2004. "Is Official Exchange Rate Intervention Effective?," Economica, London School of Economics and Political Science, vol. 71, pages 1-11, February.
    10. Hyginus Leon & Serineh Najarian, 2005. "Asymmetric adjustment and nonlinear dynamics in real exchange rates," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 10(1), pages 15-39.
    11. repec:hal:journl:halshs-00185369 is not listed on IDEAS
    12. van Tol, Michel R & Wolff, Christian C, 2005. "Forecasting the Spot Exchange Rate with the Term Structure of Forward Premia: Multivariate Threshold Cointegration," CEPR Discussion Papers 4958, C.E.P.R. Discussion Papers.
    13. Coakley, Jerry & Fuertes, Ana-Maria, 2001. "Border costs and real exchange rate dynamics in Europe," Journal of Policy Modeling, Elsevier, vol. 23(6), pages 669-676, August.
    14. Su, Fei & Chan, Kung-Sik, 2015. "Quasi-likelihood estimation of a threshold diffusion process," Journal of Econometrics, Elsevier, vol. 189(2), pages 473-484.
    15. Taylor Mark P. & Davradakis Emmanuel, 2006. "Interest Rate Setting and Inflation Targeting: Evidence of a Nonlinear Taylor Rule for the United Kingdom," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(4), pages 1-20, December.
    16. Ahmad Jameel Khadaroo, 2016. "Current Account Deficit in Mauritius: Risks and Prospects," South African Journal of Economics, Economic Society of South Africa, vol. 84(1), pages 109-128, March.
    17. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    18. Gene L. Leon & Serineh Najarian, 2003. "Asymmetric Adjustment and Nonlinear Dynamics in Real Exchange Rates," IMF Working Papers 03/159, International Monetary Fund.
    19. Chan, Ngai Hang & Yau, Chun Yip & Zhang, Rong-Mao, 2015. "LASSO estimation of threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 285-296.
    20. repec:bmo:bmoart:v:4:y:2017:i:2:p:1-16 is not listed on IDEAS

    More about this item

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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