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Numerical Issues in Threshold Autoregressive Modelling of Time Series

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

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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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. 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.
  3. 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.
  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. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
  6. 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.
  7. Kapetanios, G., 1999. "Model Selection in Threshold Models," Cambridge Working Papers in Economics 9906, Faculty of Economics, University of Cambridge.
  8. 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.
  9. Mehmet Caner & Bruce E. Hansen, 1998. "Threshold Autoregressions with a Near Unit Root," Working Papers 9821, Department of Economics, Bilkent University.
  10. 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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