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Sup-tests for linearity in a general nonlinear AR(1) model when the supremum is taken over the full parameter space

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Author Info
Francq, Christian
Horvath, Lajos
Zakoian, Jean-Michel

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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 chi-square processes and is obtained without imposing a positive lower bound for the nuisance parameter. The finite sample properties of the sup-tests are studied by simulations.

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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 16669.

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Date of creation: 2008
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Handle: RePEc:pra:mprapa:16669

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Related research
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;

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Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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    Other versions:
  2. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-72, July. [Downloadable!] (restricted)
  3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
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  4. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March. [Downloadable!] (restricted)
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  5. Lee, Lung-Fei & Chesher, Andrew, 1986. "Specification testing when score test statistics are identically zero," Journal of Econometrics, Elsevier, vol. 31(2), pages 121-149, March. [Downloadable!] (restricted)
  6. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages S119-36, Suppl. De. [Downloadable!] (restricted)
  7. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June. [Downloadable!]
  8. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Oxford University Press for Biometrika Trust, vol. 89(2), pages 484-489, June.
  9. King, Maxwell L & Shively, Thomas S, 1993. "Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 1-7, February. [Downloadable!] (restricted)
  10. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July. [Downloadable!] (restricted)
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