IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v27y2003i11p2219-2242.html
   My bibliography  Save this article

Numerical issues in threshold autoregressive modeling of time series

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188902001239
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0165-1889(02)00123-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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. 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.
    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. 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.
    8. George Kapetanios, 2001. "Model Selection in Threshold Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(6), pages 733-754, November.
    9. repec:bla:manchs:v:69:y:2001:i:6:p:623-42 is not listed on IDEAS
    10. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    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. Muhammad Jaffri Mohd Nasir & Ramzan Nazim Khan & Gopalan Nair & Darfiana Nur, 2024. "Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model," Statistical Papers, Springer, vol. 65(5), pages 2973-3006, July.
    21. 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.
    22. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. George Kapetanios, 2000. "Testing for a Unit Root against Nonlinear STAR Models," National Institute of Economic and Social Research (NIESR) Discussion Papers 164, National Institute of Economic and Social Research.
    3. Andy Snell & George Kapetanios & Yongcheol Shin, 2004. "Testing for nonlinear cointegration between stock prices and dividends," Money Macro and Finance (MMF) Research Group Conference 2003 90, Money Macro and Finance Research Group.
    4. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    5. Dueker, Michael J. & Sola, Martin & Spagnolo, Fabio, 2007. "Contemporaneous threshold autoregressive models: Estimation, testing and forecasting," Journal of Econometrics, Elsevier, vol. 141(2), pages 517-547, December.
    6. Palandri, Alessandro, 2024. "Reconciling interest rates evidence with theory: Rejecting unit roots when the HD(1) is a competing alternative," Journal of Banking & Finance, Elsevier, vol. 161(C).
    7. 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.
    8. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    9. Yunus Aksoy & Kurmas Akdogan, 2006. "Exchange Rates and Fundamentals: Is there a Role for Nonlinearities in Real Time?," Computing in Economics and Finance 2006 12, Society for Computational Economics.
    10. McMillan, David G., 2005. "Non-linear dynamics in international stock market returns," Review of Financial Economics, Elsevier, vol. 14(1), pages 81-91.
    11. Yen-Hsien Lee & Ya-Ling Huang & Hao-Jang Yang, 2012. "The Asymmetric Long-Run Relationship Between Crude Oil And Gold Futures," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 6(1), pages 9-15.
    12. Camgöz, Mevlüt & Topal, Mehmet Hanefi, 2022. "Identifying the asymmetric price dynamics of Islamic equities: Implications for international investors," Research in International Business and Finance, Elsevier, vol. 60(C).
    13. Mohcine Bakhat & Klaas WŸrzburg, 2013. "Co-integration of Oil and Commodity Prices: A Comprehensive ApproachAbstract," Working Papers fa05-2013, Economics for Energy.
    14. Richard H. Clarida & Mark P. Taylor, 2003. "Nonlinear Permanent - Temporary Decompositions in Macroeconomics and Finance," Economic Journal, Royal Economic Society, vol. 113(486), pages 125-139, March.
    15. Zacharias Bragoudakis & Dimitrios Sideris, 2019. "Asymmetric price adjustment and the effects of structural reforms in a low income environment: the case of the gasoline market in Greece," Working Papers 274, Bank of Greece.
    16. Jyh‐Lin Wu & Pei‐Fen Chen & Ching‐Nun Lee, 2009. "Purchasing Power Parity, Productivity Differentials And Non‐Linearity," Manchester School, University of Manchester, vol. 77(3), pages 271-287, June.
    17. Kleimeier, S. & Sander, H., 2002. "European financial market integration: evidence on the emergence of a single Eurozone retail banking market," Research Memorandum 060, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    18. Pelin ÖGE GÜNEY, 2013. "The Term Structure of Interest Rates: A Cointegration Analysis in the Non-Linear STAR Framework," Journal of Economics and Behavioral Studies, AMH International, vol. 5(12), pages 851-860.
    19. Sergio H. Lence & GianCarlo Moschini & Fabio Gaetano Santeramo, 2018. "Threshold cointegration and spatial price transmission when expectations matter," Agricultural Economics, International Association of Agricultural Economists, vol. 49(1), pages 25-39, January.
    20. Filippo Altissimo & Giovanni L. Violante, 2001. "The non-linear dynamics of output and unemployment in the U.S," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 461-486.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:27:y:2003:i:11:p:2219-2242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.