Francq, Christian and Horvath, Lajos and Zakoian, JeanMichel (2008): Suptests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space.

PDF
MPRA_paper_16669.pdf Download (301kB)  Preview 
Abstract
We consider linearity testing in a general class of nonlinear time series model of order 1, involving a nonnegative nuisance parameter which (i) is not identified under the null hypothesis and (ii) gives the linear model when equal to zero. This paper studies the asymptotic distribution of the Likelihood Ratio test and asymptotically equivalent supremum tests. The asymptotic distribution is described as a functional of chisquare processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite sample properties of the suptests are studied by simulations.
Item Type:  MPRA Paper 

Original Title:  Suptests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space 
Language:  English 
Keywords:  Diagnostic checking; Exponential autoregressive (EXPAR) model; Lagrange Multiplier (LM) tests; Least Squares Estimator; Likelihood Ratio (LR); Non Linear models; Supremum Tests; Smooth Transition Autoregressive (STAR); Threshold AR (TAR); Wald test 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: 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:  16669 
Depositing User:  Christian Francq 
Date Deposited:  10. Aug 2009 09:32 
Last Modified:  12. Feb 2013 00:42 
References:  Adler, R.J. (1990) An introduction to continuity, extrema, and related topics for general Gaussian processes. Institute of Mathematical Statistics Lecture Notes, Monograph Series, 12, Hayward. Andrews, D.W.K. (1993) Tests for parameter instability and structural change with unknown change point. Econometrica, 61, 821856. Andrews, D.W.K. and W. Ploberger (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica, 62, 13831414. Andrews, D.W.K. and W. Ploberger (1995) Admissibility of the likelihood ratio test when a nuisance parameter is present only under the alternative. The Annals of Statistics, 23, 16091629. Billingsley, P. (1961) The LindebergLévy theorem for martingales. Proceedings of the American Mathematical Society, 12, 788792. Billingsley, P. (1968) Convergence of probability measures. Wiley, NewYork. Chan, K.S. and H. Tong (1986) On estimating thresholds in autoregressive models. Journal of Time Series Analysis, 7, 178190. Chesher, A. (1984) Testing for neglected heterogeneity. Econometrica, 52, 865872. Davies, R.B. (1977) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 64, 247254. Davies, R.B. (1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74, 3343. Godfrey, L.G. (1988) Misspecification tests in econometrics. Cambridge university Press, Cambridge. Granger, C.W.J. and T. Teräsvirta (1993) Modelling nonlinear relationships. Oxford University Press, Oxford. Hansen, B. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica, 64, 413430. King, M. and T.S. Shively (1993) Locally optimal testing when a nuisance parameter is present only under the alternative. The Review of Economics and Statistics, 75, 17. Lee, LF and Chesher, A. (1986) Specification testing when score test statistics are identically zero. Journal of Econometrics, 31, 121149. Luukkonen, R., P. Saikkonen and T. Teräsvirta (1988) Testing linearity against smooth transition autoregressive models. Biometrika 75, 491499. Pötscher, B.M. and I.R. Prucha (1989) A uniform law of large numbers for dependent and heterogeneous data processes. Econometrica, 57, 675683. Rotnitzky, A., D. Cox, M. Bottai, and J. Robins (2000) Likelihoodbased inference with singular information matrix. Bernoulli, 6, 243284. Stinchcombe, M.B. and H. White (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory, 14, 295325. Stock, J. and Watson, M.W. (1999) A comparison of linear and nonlinear univariate models for forecasting macroeconomic times series. In R.F. Engle and H. White (eds) Cointegration, Causality and Forecasting. A festschrift in honour of Clive W.J. Granger, 144, Oxford University Press, Oxford. Teräsvirta, T. and H.M. Anderson (1992) Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics, 7, S119S136. Teräsvirta, T., D. van Dijk, and M.C. Medeiros (2004) Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: a reexamination. International Journal of Forecasting, 21, 755774. Tjøstheim, D. (1990) Nonlinear time series and Markov chains. Advances in Applied Probability, 22, 587611. Tong, H. (1990) Nonlinear time series. A dynamical system approach. Oxford University Press, Oxford. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/16669 