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Testing the adequacy of smooth transition autoregressive models. (English) Zbl 0864.62058
Summary: Smooth transition autoregressive models are a flexible family of nonlinear time series models that have also been used for modelling economic data. This paper contributes to the evaluation stage of a proposed specification, estimation, and evaluation cycle of these models by introducing a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM-type tests for the hypothesis of no remaining nonlinearity and that of parameter constancy. Small-sample properties of the \(F\) versions of these tests and some alternative test statistics are investigated by simulation. The results indicate that the proposed tests can be applied in small samples already.

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03 Parametric hypothesis testing
62P20 Applications of statistics to economics
Full Text: DOI
[1] Bacon, D. W.; Watts, D. G.: Estimating the transition between two intersecting straight lines. Biometrika 58, 525-534 (1971) · Zbl 0224.62035
[2] Breusch, T. S.; Pagan, A. R.: A simple test for heteroscedasticity and random coefficient variation. Econometrica 47, 1287-1294 (1979) · Zbl 0416.62021
[3] Godfrey, L. G.: Misspecification tests in econometrics. (1988) · Zbl 0849.62063
[4] Granger, C. W. J.; Teräsvirta, T.: Modelling nonlinear economic relationships. (1993) · Zbl 0893.90030
[5] Hjellvik, V.; Tjøstheim, D.: Nonparametric tests of linearity for time series. Biometrika 82, 351-368 (1995) · Zbl 0823.62044
[6] Klimko, L. A.; Nelson, P. I.: On conditional least squares estimation for stochastic processes. Annals of statistics 6, 629-642 (1978) · Zbl 0383.62055
[7] Lai, T. L.; Wei, C. Z.: Least squares estimates in stochastic regression models with applications in identification and control of dynamic systems. Annals of statistics 10, 154-166 (1981) · Zbl 0649.62060
[8] Lee, T. -H.; White, H.; Granger, C. W. J.: Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests. Journal of econometrics 56, 269-290 (1993) · Zbl 0766.62055
[9] Lin, C. -F.; Teräsvirta, T.: Testing the constancy of regression parameters against continuous structural change. Journal of econometrics 62, 211-228 (1994) · Zbl 0796.62054
[10] Ljung, G. M.; Box, G. E. P.: On a measure of lack-of-fit time series models. Biometrika 65, 297-303 (1978) · Zbl 0386.62079
[11] Luukkonen, R.; Saikkonen, P.; Teräsvirta, T.: Testing linearity in univariate time series models. Scandinavian journal of statistics 15, 161-175 (1988) · Zbl 0666.62089
[12] Luukkonen, R.; Saikkonen, P.; Teräsvirta, T.: Testing linearity against smooth transition autoregressive models. Biometrika 75, 491-499 (1988) · Zbl 0657.62109
[13] Teräsvirta, T.: Generalizing threshold autoregressive models. Discussion paper 90-44 (1990)
[14] Teräsvirta, T.: Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American statistical association 89, 208-218 (1994) · Zbl 1254.91686
[15] Teräsvirta, T.; Anderson, H. M.: Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of applied econometrics 7, S119-S136 (1992)
[16] Tong, H.: Non-linear time series: A dynamical system approach. (1990) · Zbl 0716.62085
[17] White, H.: Asymptotic theory for econometricians. (1984)
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