×

Third-order inference for autocorrelation in nonlinear regression models. (English) Zbl 1221.62102

Summary: We propose third-order likelihood-based methods to derive highly accurate \(p\)-value approximations for testing autocorrelated disturbances in nonlinear regression models. The proposed methods are particularly accurate for small- and medium-sized samples, whereas commonly used first-order methods like the signed log-likelihood ratio test, the M. Kobayashi test [Econometrica 59, No. 4, 1153–1159 (1991; Zbl 0741.62085)], and the standardized test can be seriously misleading in these cases. Two Monte Carlo simulations are provided to show how the proposed methods outperform the above first-order methods. An empirical example applied to US population census data is also provided to illustrate the implementation of the proposed method and its usefulness in practice.

MSC:

62J02 General nonlinear regression
62F03 Parametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
65C05 Monte Carlo methods
62H15 Hypothesis testing in multivariate analysis
91D20 Mathematical geography and demography

Citations:

Zbl 0741.62085
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Amemiya, T., The maximum likelihood and the nonlinear three-stage least squares estimator in the general nonlinear simultaneous equation model, Econometrica, 45, 955-968, (1977) · Zbl 0359.62026
[2] Amemiya, T., Advanced econometrics, (1985), Havard University Press
[3] Barndorff-Nielsen, O., Modified signed log-likelihood ratio, Biometrika, 78, 557-563, (1991) · Zbl 1192.62052
[4] Chang, F.; Wong, A.C.M., Improved likelihood-based inference for the stationary AR(2) model, Journal of statistical planning and inference, 140, 2099-2110, (2010) · Zbl 1184.62150
[5] Durbin, J.; Watson, G.S., Testing for serial correlation in least squares regression, II, Biometrika, 37, 409-428, (1950) · Zbl 0039.35803
[6] Fox, J., Nonlinear regression and nonlinear least squares, Appendix to an R and S-PLUS companion to applied regression, (2002), Sage Publication Inc.
[7] Fraser, D.; Reid, N., Ancillaries and third order significance, Utilitas Mathematica, 47, 33-53, (1995) · Zbl 0829.62006
[8] Fraser, D.; Reid, N.; Li, R.; Wong, A., p-value formulas from likelihood asymptotics: bridging the singularities, Journal of statistical research, 37, 1-15, (2003)
[9] Fraser, D.; Reid, N.; Wu, J., A simple general formula for tail probabilities for frequentist and Bayesian inference, Biometrika, 86, 249-264, (1999) · Zbl 0932.62003
[10] Gallant, A.R.; Holly, A., Statistical inference in an implicit, nonlinear, simultaneous equation model in the context of maximum likelihood estimation, Econometrica, 48, 697-720, (1980) · Zbl 0456.62022
[11] Gourieroux, C.; Monfort, A.; Trognon, A., Estimation and test in probit models with serial correlation, () · Zbl 0576.62085
[12] Hamilton, J.D., Time series analysis, (1994), Princeton University Press · Zbl 0831.62061
[13] Kobayashi, M., Testing for autocorrelated disturbances in nonlinear regression analysis, Econometrica, 59, 4, 1153-1159, (1991) · Zbl 0741.62085
[14] Lugannani, R.; Rice, S., Saddlepoint approximation for the distribution of the sums of independent random variables, Advances in applied probability, 12, 475-490, (1980) · Zbl 0425.60042
[15] Poirier, D.J.; Ruud, P.A., Probit with dependent observations, The review of economic studies, 55, 593-614, (1988) · Zbl 0652.62026
[16] Rekkas, M.; Sun, Y.; Wong, A., Improved inference for first order autocorrelation using likelihood analysis, Journal of time series analysis, 29, 3, 513-532, (2008) · Zbl 1199.62016
[17] White, K., The durbin – watson test for autocorrelation for nonlinear models, The review of economics and statistics, 74, 2, 370-373, (1992)
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.