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The comparison of optimization algorithms on unit root testing with smooth transition

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  • Omay, Tolga

Abstract

The aim of this study is to search for a better optimization algorithm in applying unit root tests that inherit nonlinear models in the testing process. The algorithms analyzed include Broyden, Fletcher, Goldfarb and Shanno (BFGS), Gauss-Jordan, Simplex, Genetic, and Extensive Grid-Search. The simulation results indicate that the derivative free methods, such as Genetic and Simplex, have advantages over hill climbing methods, such as BFGS and Gauss-Jordan, in obtaining accurate critical values for the Leybourne, Newbold and Vougos (1996, 1998) (LNV) and Sollis (2004) unit root tests. Moreover, when parameters are estimated under the alternative hypothesis of the LNV type of unit root tests the derivative free methods lead to an unbiased and efficient estimator as opposed to those obtained from other algorithms. Finally, the empirical analyses show that the derivative free methods, hill climbing and simple grid search can be used interchangeably when testing for a unit root since all three optimization methods lead to the same empirical test results.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 42129.

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Date of creation: 22 Oct 2012
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Handle: RePEc:pra:mprapa:42129

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Keywords: Nonlinear trend; Deterministic smooth transition; Structural change; Estimation methods;

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  1. Rappoport, Peter & Reichlin, Lucrezia, 1989. "Segmented Trends and Non-stationary Time Series," Economic Journal, Royal Economic Society, vol. 99(395), pages 168-77, Supplemen.
  2. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  3. Sollis, Robert & Leybourne, Stephen & Newbold, Paul, 2002. "Tests for Symmetric and Asymmetric Nonlinear Mean Reversion in Real Exchange Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 34(3), pages 686-700, August.
  4. Sollis, Robert, 2009. "A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries," Economic Modelling, Elsevier, vol. 26(1), pages 118-125, January.
  5. Bierens, Herman J., 1997. "Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate," Journal of Econometrics, Elsevier, vol. 81(1), pages 29-64, November.
  6. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  7. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  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. Robin L. Lumsdaine & David H. Papell, 1997. "Multiple Trend Breaks And The Unit-Root Hypothesis," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 212-218, May.
  10. Ucar, Nuri & Omay, Tolga, 2009. "Testing for unit root in nonlinear heterogeneous panels," Economics Letters, Elsevier, vol. 104(1), pages 5-8, July.
  11. Felix Chan & Michael McAleer, 2002. "Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 509-534.
  12. Robert Sollis, 2004. "Asymmetric adjustment and smooth transitions: a combination of some unit root tests," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 409-417, 05.
  13. Vougas, Dimitrios V., 2006. "On unit root testing with smooth transitions," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 797-800, November.
  14. Perron, Pierre, 1990. "Testing for a Unit Root in a Time Series with a Changing Mean," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 153-62, April.
  15. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
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