Testing and estimating change-points in time series

The aim of this paper is to present a few techniques which may be useful in the analysis of time series when a failure is suspected. We present two categories of tests and investigate their asymptotic properties: one, of nonparametric type, is intended to detect a general failure in spectrum; the other investigates the properties of likelihood ratio tests in parametric models which have a non-standard behaviour in this situation. Finally, we obtain the asymptotic distribution of the likelihood estimators of the change parameters.

[1]  J. Kiefer,et al.  DISTRIBUTION FREE TESTS OF INDEPENDENCE BASED ON THE SAMPLE DISTRIBUTION FUNCTION , 1961 .

[2]  Z. Birnbaum,et al.  SOME MULTIVARIATE CHEBYSHEV INEQUALITIES WITH EXTENSIONS TO CONTINUOUS PARAMETER PROCESSES , 1961 .

[3]  Ildar Ibragimov.  On Estimation of the Spectral Function of a Stationary Gaussian Process , 1963 .

[4]  T. Malevich.  The Asymptotic Behavior of an Estimate for the Spectral Function of a Stationary Gaussian Process , 1964 .

[5]  C. B. Bell,et al.  Distribution-Free Tests of Independence , 1967 .

[6]  David V. Hinkley,et al.  Inference about the change-point in a sequence of binomial variables , 1970 .

[7]  T. Anderson.  Statistical analysis of time series , 1974 .

[8]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[9]  P. Major,et al.  An approximation of partial sums of independent RV'-s, and the sample DF. I , 1975 .

[10]  P. Major,et al.  An approximation of partial sums of independent RV's, and the sample DF. II , 1975 .

[11]  D. McLeish.  Invariance principles for dependent variables , 1975 .

[12]  Alan S. Willsky,et al.  A survey of design methods for failure detection in dynamic systems , 1976, Autom..

[13]  Howell Tong,et al.  Some Comments on the Canadian Lynx Data , 1977 .

[14]  A. M. Walker,et al.  A Survey of statistical work on the Mackenzie River series of annual Canadian lynx trappings for the , 1977 .

[15]  P. Meyer,et al.  Probabilities and potential C , 1978 .

[16]  L. Shepp.  The joint density of the maximum and its location for a Wiener process with drift , 1979, Journal of Applied Probability.

[17]  Mahmoud M. Gabr,et al.  THE ESTIMATION AND PREDICTION OF SUBSET BILINEAR TIME SERIES MODELS WITH APPLICATIONS , 1981 .

[18]  E. Slud,et al.  Time Series Discrimination by Higher Order Crossings , 1982 .

[19]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[20]  Michèle Basseville,et al.  Sequential detection of abrupt changes in spectral characteristics of digital signals , 1983, IEEE Trans. Inf. Theory.

[21]  Jean Deshayes,et al.  Principe d'invariance sur le processus de vraisemblance , 1984 .