Detection of Changes in Linear Sequences

We discuss the asymptotic properties of some tests to detect possible changes in the mean of linear processes.

[1]  S. Geer,et al.  The likelihood ratio test for the change point problem for exponentially distributed random variables , 1987 .

[2]  P. Erdös,et al.  A limit theorem for the maximum of normalized sums of independent random variables , 1956 .

[3]  C. Withers.  Conditions for linear processes to be strong-mixing , 1981 .

[4]  Dawei Huang,et al.  Testing for a Change in the Parameter Values and Order of an Autoregressive Model , 1995 .

[5]  V. V. Gorodetskii,et al.  On the Strong Mixing Property for Linear Sequences , 1978 .

[6]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[7]  W. Philipp,et al.  Almost sure invariance principles for partial sums of weakly dependent random variables , 1975 .

[8]  I. B. MacNeill,et al.  The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time , 1993 .

[9]  D. Picard.  Testing and estimating change-points in time series , 1985, Advances in Applied Probability.

[10]  Walter Philipp,et al.  Almost Sure Invariance Principles for Partial Sums of Mixing $B$-Valued Random Variables , 1980 .

[11]  Edit Gombay,et al.  Asymptotic distributions of maximum likelihood tests for change in the mean , 1990 .

[12]  Ashish Sen,et al.  Some One-Sided Tests for Change in Level , 1975 .

[13]  L. Horváth,et al.  Weighted Approximations in Probability and Statistics , 1993 .

[14]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[15]  J. Bai,et al.  Least squares estimation of a shift in linear processes , 1994 .

[16]  R. Leipus,et al.  Change-point in the mean of dependent observations , 1998 .

[17]  Edit Gombay,et al.  An application of the maximum likelihood test to the change-point problem , 1994 .

[18]  K. Worsley.  Confidence regions and tests for a change-point in a sequence of exponential family random variables , 1986 .

[19]  Keith J. Worsley,et al.  On the Likelihood Ratio Test for a Shift in Location of Normal Populations , 1979 .

[20]  Lajos Horváth,et al.  Change in autoregressive processes , 1993 .

[21]  Richard A. Davis,et al.  The Asymptotic behavior of the Likelihood Ratio Statistic for Testing a Shift in Mean in a Sequence of Independent Normal Variates. , 1984 .

[22]  E. S. Page.  A test for a change in a parameter occurring at an unknown point , 1955 .

[23]  Liudas Giraitis,et al.  Testing and estimating in the change-point problem of the spectral function , 1992 .

[24]  P. Révész,et al.  Strong approximations in probability and statistics , 1981 .

[25]  I. Ibragimov,et al.  Independent and stationary sequences of random variables , 1971 .

[26]  L. Horváth,et al.  The Maximum Likelihood Method for Testing Changes in the Parameters of Normal Observations , 1993 .

[27]  Reg Kulperger,et al.  On the residuals of autoregressive processes and polynomial regression , 1985 .