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Improved likelihood-based inference for the stationary AR(2) model. (English) Zbl 1184.62150

Summary: An improved likelihood-based method based on D. A. S. Fraser et al., Biometrika 86, No. 2, 249–264 (1999; Zbl 0932.62003), is proposed to test the significance of the second lag of the stationary AR(2) model. Compared with the test proposed by J. Fan and Q. Yao [Nonlinear time series. Nonparametric and parametric methods. NY: Springer (2003; Zbl 1014.62103)] and the signed log-likelihood ratio test, the proposed method has remarkable accuracy. Simulation studies are performed to illustrate the accuracy of the proposed method. Application of the proposed method on historical data is presented to demonstrate the implementation of this method. Furthermore, the method can be extended to the general AR\((p)\) model.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)
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