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

Omay, Tolga (2012): The comparison of optimization algorithms on unit root testing with smooth transition.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Nonlinear trend; Deterministic smooth transition; Structural change; Estimation methods
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47-78.

Bierens, H.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, vol. 81, pp. 29–64.

Chan, K.S., 1993. Consistent and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model. Annals of Statistics, 520 - 533.

Chan, F., McAleer, M., 2002. Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence. Journal of Applied Econometrics17, 5, 509-534.

Dickey, D.A., Fuller W.A., 1979. Distribution of the estimates for autoregressive time series with a unit Root. Journal of the American Statistical Association 74, 427-431.

Enders, W., Granger, C. W. J., 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business and Economic Statistics 16, 304-11.

Greenaway, D., Leybourne, S. J., and Sapsford, D. 1997. Modelling growth and liberalisation using smooth transition analysis. Economic Inquiry 35, 798-814.

Kapetanios, G., Shin, Y., Snell, A., 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359-79.

Leybourne, S., Newbold, P., Vougas, D., 1998. Unit roots and smooth transitions. Journal of Time Series Analysis 19, 83–97.

Teräsvirta, T., 1994. Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89, 208-218.

Lin, C.J., Teräsvirta, T., 1994. Testing the constancy of regression parameters against continuous structural change. Journal of Econometrics 62(2), 211-228.

Lumsdaine, R. L, Papell, D. H., 1997. Multiple trend breaks and the unit root hypothesis. Review of Economics and Statistics 79 (2), 212-218.

Perron, P., 1989. The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361–1401.

Perron, P., 1990. Testing for a unit root in a time series with a changing mean. Journal of Business and Economic Statistics 8, 153-162.

Pötscher, B.M., Prucha, I.V., 1997. Dynamic Nonlinear Econometric Models – Asymptotic Theory, Berlin, Springer-Verlag

Rappaport, P., Reichlin, L., 1989. segmented trends and non-stationary time series. The Economic Journal 99, 168-177.

Sollis, R., 2004. Asymmetric adjustment and smooth transitions: a combination of some unit root tests. Journal of Time Series Analysis 25, 409-417.

Sollis, R., Leybourne, S., Newbold, P., 2002. Tests for symmetric and asymmetric nonlinear mean reversion in real exchange rates. Journal of Money Credit and Banking 34, 686-700.

Sollis, R. 2009. A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries. Economic Modelling 26, 118-125.

Tong, H., 1983. Threshold Models in Nonlinear Time Series Models. Lecture notes in Statistics, No: 21, Newyork: Siprenger-Verlag.

Ucar, N., Omay, T. 2009. Testing for unit root in nonlinear heterogeneous panels. Economics Letters 104, 5-8.

Vougas, V., D. 2006) On unit root testing with smooth transitions. Computational Statistics and Data Analysis 51, 797-800.

Zivot, E., Andrews, K., 1992. Further evidence on the great crash, the oil price shock, and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251–70.