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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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  1. Philip Rothman, 1999. "Time Series Evidence on Whether Adjustment to Long-Run Equilibrium is Asymmetric," Working Papers 9904, East Carolina University, Department of Economics.
  2. Caner,M. & Hansen,B.E., 1998. "Threshold autoregression with a near unit root," Working papers 27, Wisconsin Madison - Social Systems.
  3. Kapetanios, G., 1999. "Model Selection in Threshold Models," Cambridge Working Papers in Economics 9906, Faculty of Economics, University of Cambridge.
  4. Enders, Walter & Granger, C. W. J., 1998. "Unit Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Staff General Research Papers 1388, Iowa State University, Department of Economics.
  5. Pesaran, H.M. & Potter, S.M., 1995. "A Floor and Ceiling Model of U.S. Output," Cambridge Working Papers in Economics 9407, Faculty of Economics, University of Cambridge.
  6. 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. Kapetanios, G., 1999. "Threshold Models for Trended Time Series," Cambridge Working Papers in Economics 9905, Faculty of Economics, University of Cambridge.
  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. 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.
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Cited by:
  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. 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. H. L. Leon & Serineh Najarian, 2003. "Asymmetric Adjustment and Nonlinear Dynamics in Real Exchange Rates," IMF Working Papers 03/159, International Monetary Fund.
  4. 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.
  5. Ferrara, Laurent & Guégan, Dominique, 2005. "Detection of the industrial business cycle using SETAR models," MPRA Paper 4389, University Library of Munich, Germany.
  6. 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.
  7. 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.
  8. Norman, Stephen, 2008. "Systematic small sample bias in two regime SETAR model estimation," Economics Letters, Elsevier, vol. 99(1), pages 134-138, April.
  9. repec:hal:journl:halshs-00185369 is not listed on IDEAS
  10. 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.
  11. 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.
  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. 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.
  14. Taylor, Mark P, 2003. "Is Official Exchange Rate Intervention Effective?," CEPR Discussion Papers 3758, C.E.P.R. Discussion Papers.

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