## 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)

### Citations:

Zbl 0932.62003; Zbl 1014.62103
Full Text:

### References:

 [1] Barndorff-Nielsen, O.E., Inference on full and partial parameters based on the standardized signed log-likelihood ratio, Biometrika, 73, 307-322, (1986) · Zbl 0605.62020 [2] Barndorff-Nielsen, O.E., Modified signed log-likelihood ratio statistic, Biometrika, 78, 557-563, (1991) · Zbl 1192.62052 [3] Daniel, H.E., Tail probability approximations, International statistical review, 54, 37-48, (1987) · Zbl 0614.62016 [4] Fan, J.; Yao, Q., Nonlinear time series: nonparametric and parametric methods, (2003), Springer New York · Zbl 1014.62103 [5] Fox, J., Applied regression and generalized linear models, (2008), Sage Publications Beverley Hills, CA [6] Fraser, D.A.S., Tail probabilities from observed likelihoods, Biometrika, 77, 65-76, (1990) · Zbl 0692.62032 [7] Fraser, D.A.S.; Reid, N., Ancillaries and third order significance, Utilitas Mathematica, 47, 33-53, (1995) · Zbl 0829.62006 [8] Fraser, D.A.S.; Reid, N.; Li, R.; Wong, A.C.M., p-value formulas from likelihood asymptotics bridging the singularities, Journal of statistical research, 37, 1, 1-15, (2003) [9] Fraser, D.A.S.; 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] Judge, G.G.; Griffiths, W.E.; Hill, R.C.; Lutkepohl, H.; Lee, T.C., The theory and practice of econometrics, (1985), Wiley New York [11] Levenbach, H., Estimation of autoregressive parameters from a marginal likelihood function, Biometrika, 59, 1, 61-71, (1972) · Zbl 0232.62031 [12] Lugannani, R.; Rice, S., Saddlepoint approximation for the distribution of the sum of independent random variables, Advanced applied probability, 12, 475-490, (1980) · Zbl 0425.60042 [13] McNeil, D.R., Interactive data analysis, (1977), Wiley New York · Zbl 0777.62005 [14] Rekkas, M.; Sun, Y.; Wong, A.C.M., Improved inference for first-order autocorrelation using likelihood analysis, Journal of time series analysis, 29, 513-532, (2008) · Zbl 1199.62016 [15] Schervish, M.J., Theory of statistics, (1995), Springer New York · Zbl 0834.62002
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.