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Numerical issues in threshold autoregressive modeling of time series

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  • Coakley, Jerry
  • Fuertes, Ana-Marı́a
  • Pérez, Marı́a-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.

Suggested Citation

  • Coakley, Jerry & Fuertes, Ana-Marı́a & Pérez, Marı́a-Teresa, 2003. "Numerical issues in threshold autoregressive modeling of time series," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2219-2242.
    • Handle: RePEc:eee:dyncon:v:27:y:2003:i:11:p:2219-2242
    DOI: 10.1016/S0165-1889(02)00123-9
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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.
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    3. 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.
    4. Philip Rothman, 1999. "Time Series Evidence on Whether Adjustment to Long-Run Equilibrium is Asymmetric," Working Papers 9904, East Carolina University, Department of Economics.
    5. George Kapetanios, 2001. "Model Selection in Threshold Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 733-754, November.
    6. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    7. Jerry Coakley & Ana‐Maria Fuertes, 2001. "A Non‐Linear Analysis of Excess Foreign Exchange Returns," Manchester School, University of Manchester, vol. 69(6), pages 623-642, December.
    8. 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.
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    10. 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.
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    Citations

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    Cited by:

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    2. Anne Peguin-Feissolle & Gilles Dufrénot & Dominique Guegan, 2006. "Changing-regime volatility : A fractionally integrated SETAR model," Working Papers halshs-00410540, HAL.
    3. Wolff, Christian & van Tol, Michel R, 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.
    4. 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.
    5. 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.
    6. 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.
    7. Zarina Oflaz, 2017. "Structural Break, Nonlinearity and the Hysteresis hypothesis: Evidence from new unit root tests," Econometrics Letters, Bilimsel Mektuplar Organizasyonu (Scientific letters), vol. 4(2), pages 1-16.
    8. Mr. Gene L. Leon & Serineh Najarian, 2003. "Asymmetric Adjustment and Nonlinear Dynamics in Real Exchange Rates," IMF Working Papers 2003/159, International Monetary Fund.
    9. 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.
    10. Coakley, Jerry & Fuertes, Ana-Maria, 2006. "Testing for sign and amplitude asymmetries using threshold autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 623-654, April.
    11. Omay, Tolga & Shahbaz, Muhammad & Stewart, Chris, 2021. "Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test," MPRA Paper 107691, University Library of Munich, Germany, revised 10 May 2021.
    12. 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.
    13. 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.
    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. Norman, Stephen, 2008. "Systematic small sample bias in two regime SETAR model estimation," Economics Letters, Elsevier, vol. 99(1), pages 134-138, April.
    16. 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.
    17. 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.
    18. Chun Yip Yau & Chong Man Tang & Thomas C. M. Lee, 2015. "Estimation of Multiple-Regime Threshold Autoregressive Models With Structural Breaks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1175-1186, September.
    19. Taylor, Mark, 2003. "Is Official Exchange Rate Intervention Effective?," CEPR Discussion Papers 3758, C.E.P.R. Discussion Papers.
    20. 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.
    21. 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.

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    More about this item

    Keywords

    Band-TAR; QR factorization; Givens rotations; Rational interpolation;
    All these keywords.

    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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