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Numerical Issues in Threshold Autoregressive Modelling of Time Series

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

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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File URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfri/rsrchcentres/ferc/wrkingpaprseries/fwp01-09.pdf
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Bibliographic Info

Paper provided by Warwick Business School, Finance Group in its series Working Papers with number wp01-09.

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Date of creation: 2001
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Handle: RePEc:wbs:wpaper:wp01-09

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References

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  1. 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.
  2. 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 304-11, July.
  3. Kapetanios, G., 1999. "Model Selection in Threshold Models," Cambridge Working Papers in Economics 9906, Faculty of Economics, University of Cambridge.
  4. Kapetanios, G., 1999. "Threshold Models for Trended Time Series," Cambridge Working Papers in Economics 9905, Faculty of Economics, University of Cambridge.
  5. 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.
  6. Nathan S. Balke & Thomas B. Fomby, 1992. "Threshold cointegration," Research Paper 9209, Federal Reserve Bank of Dallas.
    • 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 627-45, August.
  7. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
  8. Coakley, Jerry & Fuertes, Ana-Maria, 2001. "A Non-linear Analysis of Excess Foreign Exchange Returns," Manchester School, University of Manchester, vol. 69(6), pages 623-42, December.
  9. Philip Rothman, 1999. "Time Series Evidence on Whether Adjustment to Long-Run Equilibrium is Asymmetric," Working Papers 9904, East Carolina University, Department of Economics.
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Citations

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Cited by:
  1. Gilles Dufrénot & Dominique Guegan & Anne Peguin-Feissolle, 2005. "Long-memory dynamics in a SETAR model - Applications to stock markets," Post-Print halshs-00179339, HAL.
  2. repec:hal:cesptp:halshs-00185369 is not listed on IDEAS
  3. 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.
  4. 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.
  5. Laurent Ferrara & Dominique Guégan, 2005. "Detection of the Industrial Business Cycle using SETAR Models," Journal of Business Cycle Measurement and Analysis, OECD Publishing,CIRET, vol. 2005(3), pages 353-371.
  6. H. L. Leon & Serineh Najarian, 2003. "Asymmetric Adjustment and Nonlinear Dynamics in Real Exchange Rates," IMF Working Papers 03/159, International Monetary Fund.
  7. repec:hal:journl:halshs-00185369 is not listed on IDEAS
  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. Norman, Stephen, 2008. "Systematic small sample bias in two regime SETAR model estimation," Economics Letters, Elsevier, vol. 99(1), pages 134-138, April.
  10. Anne Peguin-Feissolle & Gilles Dufrénot & Dominique Guegan, 2006. "Changing-regime volatility : A fractionally integrated SETAR model," Working Papers halshs-00410540, HAL.
  11. 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.
  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. Taylor, Mark P, 2003. "Is Official Exchange Rate Intervention Effective?," CEPR Discussion Papers 3758, C.E.P.R. Discussion Papers.
  14. 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.
  15. 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.

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