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Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise |
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| Authors: | Brouste Alexandre Cai Chunhao Soltane Marius Wang Longmin |
| Institution: | 1.Laboratoire Manceau de Mathématiques, Le Mans Université, Avenue Olivier Messiaen, 72085, Le Mans Cedex 9, France ;2.School of Mathematics, Shanghai University of Finance and Economics, No.777 Guoding road, Yangpu district, Shanghai, China ;3.School of Mathematical Science, Nankai University, No. 94 Weijin Road, Nankai district, Tianjin, China ; |
| Abstract: | The likelihood ratio test for a change in the mean-reverting parameter of a first order autoregressive model with stationary Gaussian noise is considered. The test statistic converges in distribution to the Gumbel extreme value distribution under the null hypothesis of no change-point for a large class of covariance structures including long-memory processes as the fractional Gaussian noise. |
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