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The Bierens test under data dependence. (English) Zbl 0855.62073
Summary: This paper generalizes the consistent model specification test proposed by H. J. Bierens [Econometrica 58, No. 6, 1443-1458 (1990; Zbl 0737.62058)] to the framework of time series. The main problem encountered in this generalization is the fact that time series usually are functions of an infinite number of random variables. A simulation procedure that is capable of establishing asymptotically valid critical values for such a test is described.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F05 Asymptotic properties of parametric tests
62E20 Asymptotic distribution theory in statistics
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[1] Andrews, D. W. K.: Consistency in nonlinear econometric models: A generic uniform law of large numbers. Econometrica 55, 1465-1471 (1987) · Zbl 0646.62101
[2] Andrews, D. W. K.: Generic uniform convergence. Econometric theory 8, 241-257 (1992)
[3] Bierens, H. J.: Robust methods and asymptotic theory in nonlinear econometrics. (1981) · Zbl 0461.62086
[4] Bierens, H. J.: Consistent model specification tests. Journal of econometrics 20, 105-134 (1982) · Zbl 0549.62076
[5] Bierens, H. J.: Model specification testing of time series regressions. Journal of econometrics 26, 323-353 (1984) · Zbl 0563.62064
[6] Bierens, H. J.: ARMAX model specification testing, with an application to unemployment in The Netherlands. Journal of econometrics 35, 161-191 (1987) · Zbl 0621.62106
[7] Bierens, H. J.: Arma memory index modeling of economic time series. Econometric theory 4, 35-59 (1988)
[8] Bierens, H. J.: A consistent conditional moment test of functional form. Econometrica 58, 1443-1458 (1990) · Zbl 0737.62058
[9] Bierens, H. J.: Least squares estimation of linear and nonlinear armax models under data heterogeneity. Annales d’economie et de statistique 20/21, 143-169 (1991)
[10] Bierens, H. J.: Topics in advanced econometrics; estimation, testing, and specification of cross-section and time series models. (1994) · Zbl 0806.62093
[11] Bierens, H. J.; Hartog, J.: Nonlinear regression with discrete explanatory variables, with an application to the earnings function. Journal of econometrics 38, 269-299 (1988) · Zbl 0699.62065
[12] Bierens, H. J.; Ploberger, W.: Asymptotic optimality of integrated conditional moment tests. (1994) · Zbl 0927.62085
[13] Gallant, A. R.; Nychka, D. W.: Semi-nonparametric maximum likelihood estimation. Econometrica 55, 363-390 (1987) · Zbl 0631.62110
[14] Gallant, A.R. and H. White, A unified theory of estimation and inference for nonlinear dynamic models (Basil Blackwell, New York, NY).
[15] Giné, E.; Zinn, J.: Bootstrapping general empirical measures. Annals of probability 18, 851-869 (1990) · Zbl 0706.62017
[16] Hansen, B. E.: Inference when a nuisance parameter is not identified under the null hypo-thesis. Center for economic research working paper 296 (1992)
[17] Jennrich, R. I.: Asymptotic properties of nonlinear least squares estimators. Annals of mathematical statistics 40, 633-643 (1969) · Zbl 0193.47201
[18] Narasimhan, R.: Several complex variables. (1971) · Zbl 0223.32001
[19] Newey, W. K.: Maximum likelihood specification testing and conditional moment tests. Econometrica 53, 1047-1070 (1985) · Zbl 0629.62107
[20] Pollard, D.: Empirical processes: theory and applications. CBMS regional conference series in probability and statistics 2 (1990) · Zbl 0741.60001
[21] Pötscher, B. M.; Prucha, I. R.: Basic structure of the asymptotic theory in dynamic nonlinear econometric models, part 1: consistency and approximation concepts. Econometric reviews 10, 125-216 (1991) · Zbl 0737.62096
[22] Royden, H. L.: Real analysis. (1988) · Zbl 0704.26006
[23] Stinchcombe, M. B.; White, H.: Consistent specification testing using duality. (1992)
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