Detecting change-points in Markov chains

Markov chains provide a flexible model for dependent random variables with applications in such disciplines as physics, environmental science and economics. In the applied study of Markov chains, it may be of interest to assess whether the transition probability matrix changes during an observed realization of the process. If such changes occur, it would be of interest to estimate the transitions where the changes take place and the probability transition matrix before and after each change. For the case when the number of changes is known, standard likelihood theory is developed to address this problem. The bootstrap is used to aid in the computation of p-values. When the number of changes is unknown, the AIC and BIC measures are used for model selection. The proposed methods are studied empirically and are applied to example sets of data.

[1]  A. Gottschau.  Exchangeability in multivariate Markov chain models. , 1992, Biometrics.

[2]  Fred Godtliebsen,et al.  Multiscale spectral analysis for detecting short and long range change points in time series , 2008, Comput. Stat. Data Anal..

[3]  Benjamin Yakir,et al.  Optimal detection of a change in distribution when the observations form a Markov chain with a finite state space , 1994 .

[4]  A. Madansky.  TESTS OF HOMOGENEITY FOR CORRELATED SAMPLES , 1963 .

[5]  P. Billingsley,et al.  Statistical Methods in Markov Chains , 1961 .

[6]  Timothy R. C. Read,et al.  Multinomial goodness-of-fit tests , 1984 .

[7]  R. C. Dahiya.  Integer-parameter estimation in discrete distributions , 1986 .

[8]  T. W. Anderson,et al.  Statistical Inference about Markov Chains , 1957 .

[9]  A. Pewsey.  Exploring the Limits of Bootstrap , 1994 .

[10]  Testing homogeneity over time of a parameter of a markov sequence , 1997 .

[11]  M. Bartlett.  The frequency goodness of fit test for probability chains , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[13]  P. Turchin,et al.  Modelling the effect of host patch size on Mexican bean beetle emigration , 1986 .

[14]  H. Akaike.  A new look at the statistical model identification , 1974 .

[15]  L. Horváth,et al.  Limit Theorems in Change-Point Analysis , 1997 .

[16]  Patrick Billingsley,et al.  Statistical inference for Markov processes , 1961 .

[17]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[18]  Kevin Geary.  Indicators of educational progress: a Markov chain approach applied to Swaziland , 1978 .

[19]  W. A. V. Clark,et al.  MARKOV CHAIN ANALYSIS IN GEOGRAPHY: AN APPLICATION TO THE MOVEMENT OF RENTAL HOUSING AREAS , 1965 .

[20]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.