## 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

### Keywords:

likelihood analysis; $$p$$-value

Zbl 0741.62085
Full Text:

### References:

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