Picard, Dominique Testing and estimating change-points in time series. (English) Zbl 0585.62151 Adv. Appl. Probab. 17, 841-867 (1985). The paper is devoted to the following two problems: (i) Detecting a change in a time series which does not affect the mean but changes the covariance structure. A procedure related to the Kolmogorov-Smirnov test is proposed. (ii) Detecting a change of the mean and covariance of an autoregressive process. The asymptotic behaviour of the likelihood ratio test and the asymptotic distribution of the maximum likelihood estimators of the change parameters are investigated. Reviewer: J.Anděl Cited in 4 ReviewsCited in 100 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F05 Asymptotic properties of parametric tests 62F12 Asymptotic properties of parametric estimators Keywords:change-point problem; failure in spectrum; stationary processes; Brownian motion; time series; covariance structure; Kolmogorov-Smirnov test; mean; autoregressive process; likelihood ratio test; asymptotic distribution of the maximum likelihood estimators PDFBibTeX XMLCite \textit{D. Picard}, Adv. Appl. Probab. 17, 841--867 (1985; Zbl 0585.62151) Full Text: DOI