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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.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F03 Parametric hypothesis testing 62P20 Applications of statistics to economics
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##### References:
 [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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