Landajo, Manuel and Presno, María José (2010): Nonparametric pseudoLagrange multiplier stationarity testing.

PDF
MPRA_paper_25659.pdf Download (403kB)  Preview 
Abstract
The framework of stationarity testing is extended to allow a generic smooth trend function estimated nonparametrically. The asymptotic behavior of the pseudoLagrange Multiplier test is analyzed in this setting. The proposed implementation delivers a consistent test whose limiting null distribution is standard normal. Theoretical analyses are complemented with simulation studies and some empirical applications.
Item Type:  MPRA Paper 

Original Title:  Nonparametric pseudoLagrange multiplier stationarity testing 
Language:  English 
Keywords:  Time series, stationarity testing, limiting distribution, nonparametric regression, nonparametric hypothesis testing 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C14  Semiparametric and Nonparametric Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes 
Item ID:  25659 
Depositing User:  María José Presno 
Date Deposited:  08. Oct 2010 11:11 
Last Modified:  12. Feb 2013 18:35 
References:  Amsler, C., Schmidt, P. and Vogelsang, T.J., 2009. The KPSS test using fixedb critical values: size and power in highly autocorrelated time series. Journal of Time Series Econometrics 1(1), Article 5. doi 10.2202/19411928 1027. Anderson, T.W., 1971. The Statistical Analysis of Time Series. John Wiley & Sons, New York. Becker, R., Enders, W. and Lee, J., 2006. A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis 27, 381409. Bhansali, R.J., Giraitis, L. and Kokoszka, P.S., 2007. Convergence of quadratic forms with nonvanishing diagonal. Statistics & Probability Letters 77, 726734. 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 81, 2964. Billingsley, P., 1968. Convergence of Probability Measures. John Wiley & Sons, New York. Brooks, C., 2008. Introductory Econometrics for Finance. Cambridge University Press, Cambridge. Busetti, F. and Harvey, A.C., 2001. Testing for the presence of a random walk in series with structural breaks. Journal of Time Series Analysis 22, 127150. 639657. Caner, M. and Hansen, B.E., 2001. Threshold autoregressions with a unit root. Econometrica 69, 15551596. DiCecio, R., Engemann, K.M., Owyang, M.T. and Wheeler, C.H., 2008. Changing trends in the labor force: a survey. Federal Reserve Bank of St. Louis Review 90, 4762. Diebold, F.X. and Kilian, L., 2000. Unitroot tests are useful for selecting forecasting models. Journal of Business and Economics Statistics 18, 265273. Dore, M.H.I. and Johnston, M., 2000. The carbon cycle and the value of forests as a carbon sink: a boreal case study. In Sustainable Forest Management and Global Climate Change: Selected Case Studies from the Americas. Edward Elgar Publishing, Cheltenham, UK. Enders, W. and Granger, C.W.J., 1998. Unitroot tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business and Economic Statistics 16, 304311. Enders, W. and Lee, J., 2004. Testing for a unit root with a nonlinear Fourier function. Mimeo, University of Alabama. Escanciano, J.C., 2006. Goodnessoffit tests for linear and nonlinear time series models. Journal of the American Statistical Association 101, 531541. Gallant, A.R., 1987. Nonlinear Statistical Models. John Wiley & Sons, New York. GayGarcia, C., Estrada, F. and Sánchez, A., 2009. Global and hemispheric temperatures revised. Climatic Change 94, 333349. Van Gelder, P.H.A.J.M., Wang, W. and Vrijling, J.K., 2007. Statistical estimation methods for extreme hydrological events. In Extreme Hydrological Events: New Concepts for Security. Springer Netherlands. Grenander, U., 1981. Abstract inference. John Wiley & Sons, New York. Gustavsson, M. and Österholm, P., 2006. The informational value of unemployment statistics: a note on the time series properties of participation rates. Economics Letters 92, 428433. Gustavsson, M. and Österholm, P., 2010. Laborforce participation rates and the informational value of unemployment rates: evidence from disaggregated US data. Working paper 2010:14. Departament of Economics, Uppsala Universitet. (avalaible at: http://www.nek.uu.se) Harvey, D.I., Leybourne, S.J. and Taylor, A.M.R., 2009. Unit root testing in practice: dealing with uncertainty over the trend and initial conditions. Econometric Theory 25, 587636. Harvey, D.I. and Mills, T.C., 2004. Tests for stationarity in series with endogenously determined structural change. Oxford Bulletin of Economics and Statistics 66, 863894. Hashimzade, N. and Vogelsang, T.J., 2008. Fixedb asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators. Journal of Time Series Analysis 29, 142162. Hobijn, B., Franses, P.H. and Ooms, M., 2004. Generalizations of the KPSStest for stationarity. Statistica Neerlandica 58, 483502. Hong, Y. and Lee Y.J., 2003. Generalized spectral tests for conditional mean models in time series with conditional heteroscedasticity of unknown form. Review of Economic Studies 72, 499541. Hong, Y. and White, H., 1995. Consistent specification testing via nonparametric series regression. Econometrica 63, 11331159. Jewell, T., Lee, J., Tieslau, M. and Stracizich, M.C., 2003. Stationarity of health expenditures and GDP: evidence from panel unit root tests with heterogeneous structural breaks. Journal of Health Economics 22, 313323. Kapetanios, G., Shin, Y. and Snell, A., 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359379. Kiefer, N.M. and Vogelsang, T.J., 2005. A new asymptotic theory for heteroskedasticity and autocorrelation robust tests. Econometric Theory 21,11301164. Kurozumi, E., 2002. Testing for stationarity with a break. Journal of Econometrics 108, 6399. Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y., 1992. Testing the null hypothesis of stationarity against the alternative of a unit root. How sure are we that economic time series have a unit root? Journal of Econometrics 54, 159178. Landajo, M. and Presno, M.J., 2010. Stationarity testing under nonlinear models. Some asymptotic results. Journal of Time Series Analysis 31, 392405. Lee, J. and Strazicich, M., 2001. Testing the null of stationarity in the presence of a structural break. Applied Economics Letters 8, 377382. Lee, J. and Strazicich, M., 2003. Minimum Lagrange Multiplier unit root with two structural breaks. Review of Economics and Statistics 85, 10821089. Leybourne, S.J., and McCabe, B.P.M., 1994. A consistent test for a unit root. Journal of Business and Economics Statistics 12, 157166. Leybourne, S., Newbold, P. and Vougas, D., 1998. Unit roots and smooth transition. Journal of Time Series Analysis 19, 8397. MacNeill, I.B., 1978. Properties of sequences of partial sums of polynomial regression residuals with applications to tests for change of regression at unknown times. Annals of Statistics 6 (2), 422433. Madsen, J., Mishra, V. and Smyth, R., 2008. Are labour force participation rates nonstationary? Evidence from 130 years for G7 countries. Australian Economic Papers 47, 166189. Mills, T.C. and Markellos, R.N., 2008. The Econometric Modelling of Financial Time Series. Cambridge University Press, Cambridge. Nabeya, S. and Tanaka, K., 1988. Asymptotic theory of a test for the constancy of regression coefficients against the random walk alternative. The Annals of Statistics 16, 218235. Nelson, C.R. and Plosser, C.I., 1982. Trends and random walks in macroeconomic time series: some evidence and implications. Journal of Monetary Economics 10, 139162. Perron, P., 1989. The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 13611401. Perron, P., 2006. Dealing with Structural Breaks. In Palgrave Handbook of Econometrics, Vol. 1: Econometric Theory, Patterson, K. and T.C. Mills (eds.), Palgrave Macmillan, 278352. Phillips, P.C.B., 2005. HAC estimation by automated regression. Econometric Theory 21, 116142. Pötscher, B.M. and Prucha, I.R., 1991. Basic structure of the asymptotic theory in dynamic nonlinear econometric models, part II: asymptotic normality. Econometric Reviews 10, 253325. Presno, M.J. and Landajo, M., 2010. Computation of limiting distributions in stationarity testing with a generic trend. Metrika 71, 165183. Rodrigues, P.M.M. and Taylor, A.M. R., 2009. The flexible Fourier form and local GLS detrend unit root tests. Bank of Portugal Working Paper 200919. Sollis, R., 2004. Asymmetric adjustment and smooth transitions: a combination of some unit root tests. Journal of Time Series Analysis 25, 409417. Sul, D., Phillips, P.C.B. and Choi, C., 2005. Prewhitening bias in HAC estimation. Oxford Bulletin of Economics and Statistics 67, 517546. Sun, Y.X., Phillips, P.C.B. and Jin, S., 2008. Optimal bandwidth selection in heteroskedasticityautocorrelation robust testing. Econometrica 76, 175194. Tanaka, K., 1990. The Fredholm approach to asymptotic inference on nonstationary and noninvertible time series models. Econometric Theory 6, 411432. Tanaka, K., 1996. Time Series Analysis: Nonstationary and Noninvertible Distribution Theory. John Wiley & Sons, New York. Teräsvirta, T., 2005. Forecasting economic variables with nonlinear models. SSE/EFI Working Paper Series in Economics and Finance, Nº 598. Stockholm School of Economics. Wang, W., 2006. Stochasticity, Nonlinearity and Forecasting of Streamflow Processes. IOS Press, Amsterdam. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/25659 