zbMATH — the first resource for mathematics

Consistent model specification tests for time series econometric models. (English) Zbl 0929.62054
Summary: We consider general hypothesis testing problems for nonparametric and semiparametric time-series econometric models. We apply the general methodology to construct a consistent test for omitted variables and a consistent test for a partially linear model. The proposed tests are shown to have asymptotic normal distributions under their respective null hypotheses. We also discuss the problems of testing portfolio conditional mean-variance efficiency and testing a semiparametric single index model. Monte Carlo simulations are conducted to examine the finite sample performances of the nonparametric omitted variable test and the test for a partially linear specification.

62G10 Nonparametric hypothesis testing
91B84 Economic time series analysis
62G20 Asymptotic properties of nonparametric inference
62P05 Applications of statistics to actuarial sciences and financial mathematics
62P20 Applications of statistics to economics
Full Text: DOI
[1] Ait-Sahalia, Y., Bickel, P.J., Stoker, T.M., 1994. Goodness-of-fit tests for regression using kernel methods. Manuscript, University of Chicago. · Zbl 1004.62042
[2] Andrews, D.W.K., 1997. A conditional Kolmogorov test. Econometrica 65, 1097-1128. · Zbl 0928.62019
[3] Bierens, H.J, Consistent model specification tests, Journal of econometrics, 20, 105-134, (1982) · Zbl 0549.62076
[4] Bierens, H.J, A consistent conditional moment test of functional form, Econometrica, 58, 1443-1458, (1990) · Zbl 0737.62058
[5] Bierens, H.J., Ploberger, W., 1997. Asymptotic theory of integrated conditional moment tests. Econometrica, 65, 1129-1154. · Zbl 0927.62085
[6] Bollerslev, T, Generalized autoregressive conditional heteroskedasticity, Journal of econometrics, 31, 307-327, (1986) · Zbl 0616.62119
[7] Chen, X., Fan, Y., 1997. Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series, forthcoming in Journal of Econometrics. · Zbl 1041.62506
[8] Christoffersen, P., Hahn, J., 1997. Nonparametric testing of ARCH for option pricing. Unpublished manuscript.
[9] Cochrane, J, A cross-sectional test of an investment-based asset pricing model, Journal of political economy, 104, 572-621, (1996)
[10] DeJong, P, A central limit theorem for generalized quadratic forms, Probability theory and related fields, 75, 261-277, (1987)
[11] Delgado, M.A; Stengos, T, Semiparametric testing of non-nested econometric models, Review of economic studies, 75, 345-367, (1994)
[12] Denker, M., Keller, G., 1983. On U-statistics and v. Mises statistics for weakly dependent processes. Zeitschrift Wahrscheinlichkeitstheorie verw, Gebiete 64, 505-522. · Zbl 0519.60028
[13] Engle, R.F, Autoregressive conditional heteroskedasticity with estimates of the variance of united kingdom inflation, Econometrica, 50, 987-1008, (1982) · Zbl 0491.62099
[14] Engle, R.F; Granger, C.W.J; Rice, J; Weiss, A, Semiparametric estimation of the relation between weather and electricity sales, Journal of the American statistical association, 81, 310-320, (1986)
[15] Eubank, R; Hart, J, Testing goodness-of-fit in regression via order selection criteria, The annals of statistics, 20, 1412-1425, (1992) · Zbl 0776.62045
[16] Eubank, R; Spiegelman, S, Testing the goodness of fit of a linear model via nonparametric regression techniques, Journal of the American statistical association, 85, 387-392, (1990) · Zbl 0702.62037
[17] Fan, Y., Li, Q., 1992. The asymptotic expansion for the kernel sum of squared residuals and its applications in hypotheses testing. Manuscript, University of Windsor.
[18] Fan, Y., Li, Q., 1996a. Consistent model specification tests: omitted variables, parametric and semiparametric functional forms. Econometrica 64, 865-890. · Zbl 0854.62038
[19] Fan, Y., Li, Q., 1996b. Central limit theorem for degenerate U-statistics of absolutely regular processes with applications to model specification tests. Journal of Nonparametric Statistics, forthcoming.
[20] Fan, Y., Li, Q., 1996c. Root-N-consistent estimation of partially linear time series models. Journal of Nonparametric Statistics, forthcoming. · Zbl 0953.62094
[21] Gibbons, M; Ferson, W, Testing asset pricing models with changing expectations and an unobservable market portfolio, Journal of financial economics, 14, 217-236, (1985)
[22] Gibbons, M; Ross, S; Shanken, J, A test of the efficiency of a given portfolio, Econometrica, 57, 1121-1152, (1989) · Zbl 0679.62097
[23] Gourieroux, C; Holly, A; Monfort, A, Likelihood ratio test, Wald test, and kuhn – tucker test in linear models with inequality constraints on the regression parameters, Econometrica, 50, 63-80, (1982) · Zbl 0483.62058
[24] Gozalo, P.L, A consistent model specification test for nonparametric estimation of regression function models, Econometric theory, 9, 451-477, (1993)
[25] Hall, P, Central limit theorem for integrated square error of multivariate nonparametric density estimators, Journal of multivariate analysis, 14, 1-16, (1984) · Zbl 0528.62028
[26] Hansen, B.E, Inference when a nuisance parameter is not identified under the null hypothesis, Econometrica, 64, 413-430, (1996) · Zbl 0862.62090
[27] Härdle, W; Mammen, E, Comparing nonparametric versus parametric regression fits, The annals of statistics, 21, 1926-1947, (1993) · Zbl 0795.62036
[28] Hong, Y; White, H, Consistent specification testing via nonparametric series regression, Econometrica, 63, 1133-1159, (1995) · Zbl 0941.62125
[29] Horowitz, J.L; Härdle, W, Testing a parametric model against a semiparametric alternative, Econometric theory, 10, 821-848, (1994)
[30] Hsiao, C., Li, Q., 1997. A consistent test for conditional heteroskedasticity in time-series regression models. Manuscript. · Zbl 0976.62087
[31] Lavergne, P., Vuong, Q., 1996a. Nonparametric selection of regressors: the nonnested case. Econometrica 64, 207-219. · Zbl 0860.62039
[32] Lavergne, P., Vuong, Q., 1996b. Nonparametric significance testing. Manuscript. · Zbl 0968.62047
[33] Lewbel, A., 1993. Consistent tests with nonparametric components with an application to Chinese production data. Manuscript, Brandeis University.
[34] Lewbel, A, Consistent nonparametric testing with an application to testing slusky symmetry, Journal of econometrics, 67, 379-401, (1995) · Zbl 0820.62042
[35] Li, Q., 1994. Some simple consistent tests for a parametric model versus semiparametric or nonparametric alternatives. Manuscript.
[36] Li, Q., Wang, S., 1998. A simple consistent bootstrap test for a parametric regression functional form. Journal of Econometrics, 87, 145-165. · Zbl 0943.62031
[37] Linton, O., Gozalo, P.L., 1997. Consistent testing of additive models. Manuscript.
[38] Newey, W.K, Maximum likelihood specification testing and conditional moment tests, Econometrica, 53, 1047-1070, (1985) · Zbl 0629.62107
[39] Politis, D.N; Romano, J.P, The stationary bootstrap, Journal of the American statistical association, 89, 1303-1313, (1994) · Zbl 0814.62023
[40] Powell, J.L; Stock, J.H; Stoker, T.M, Semiparametric estimation of index coefficients, Econometrica, 57, 6, 1403-1430, (1989) · Zbl 0683.62070
[41] Robinson, P.M, Root-N-consistent semiparametric regression, Econometrica, 56, 4, 931-954, (1988) · Zbl 0647.62100
[42] Robinson, P.M, Hypothesis testing in semiparametric and nonparametric models for econometric time series, Review of economic studies, 56, 511-534, (1989) · Zbl 0681.62101
[43] Robinson, P.M, Consistent nonparametric entropy-based testing, Review of economic studies, 58, 437-453, (1991) · Zbl 0719.62055
[44] Stock, J.H., 1989. Nonparametric policy analysis. Journal of the American Statistical Association 84, 567-575.
[45] Tauchen, G, Diagnostic testing and evaluation of maximum likelihood models, Journal of econometrics, 30, 415-443, (1985) · Zbl 0591.62094
[46] Ullah, A, Specification analysis of econometric models, Journal of quantitative economics, 2, 187-209, (1985)
[47] Whang, Y.J; Andrews, D.W.K, Tests of specification for parametric and semiparametric models, Journal of econometrics, 57, 277-318, (1993) · Zbl 0786.62029
[48] Wooldridge, J, A test for functional form against nonparametric alternatives, Econometric theory, 8, 452-475, (1992)
[49] Yatchew, A.J, Nonparametric regression tests based on least squares, Econometric theory, 8, 435-451, (1992)
[50] Wang, Q., 1997. A nonparametric test of the conditional mean-variance efficiency. Ph.D Thesis. University of Chicago.
[51] Zheng, J.X, A consistent test of functional form via nonparametric estimation technique, Journal of econometrics, 75, 263-289, (1996) · Zbl 0865.62030
[52] Zheng, J.X., 1998a. Consistent specification testing for conditional symmetry. Econometric Theory 14, 139-149.
[53] Zheng, J.X., 1998b. A specification test of conditional parametric distribution using kernel estimation methods. Manuscript.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.