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.


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


Zbl 0741.62085
Full Text: DOI


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