BAYESIAN INFERENCE TO MULTIPLE CHANGES IN THE VARIANCE OF AR(p) TIME SERIES MODEL
Keywords:
Time Series Model, Autoregressive Model, Variance Change, Posterior Distribution.Abstract
The problem of a change in the mean of a sequence of random variables at an unknown time point has been addressed extensively in the literature. But, the problem of a change in the variance at an unknown time point has, however, been covered less widely. This paper analyses a sequence of autoregressive, AR(p), time series model in which the variance may be subjected to multiple changes at an unknown time points. Posterior distributions are found both for the unknown points of time at which the changes occurred and for the parameters of the model. A numerical example is also discussed.
Downloads
References
Box, G.E.P. and Jenkins, G.M. (1970). Time Series Analysis, Forecasting and
Control, Holden Day, San Francisco.
Broemeling, L.D. (1972). Bayesian procedure for detecting a change in a
sequence of random variables, Metron, XXX-N-1-4, p. 1-14.
Broemeling, L.D. (1974). Bayesian inference about a changing a sequence of
random variables, Communications in Statistics, 3(3), p. 243-255.
Broemeling, L.D. (1985). Bayesian Analysis of Linear Models. Marcel Dekker
Inc., New York and Basel.
Chernoff, R.L. and S. Zacks (1964). Estimating the current mean of a normal
distribution which is subjected to changes over time, Annals of Mathematical
Statistics, 35, p. 999-1018.
Hinkley, D.V. (1971). Inference about the change-point from cumulative sum
tests, Biometrika, 58, p. 509-523.
Holbert, D. (1982). A Bayesian analysis of a switching linear model, Journal
of Econometrics, 19, p. 77-87.
Hsu, D.A. (1977). Tests for variance shift at an unknown time point, Journal of
the Royal Statistical Society-C, 26, p. 279-284.
Kohn, P. and Kohn, R. (2008). Efficient Bayesian inference for multiple
change-point and mixture innovation models, Journal of Business and
Economic Statistics, 26(1), p. 66-77.
Lee, A.F.S. and Heghinian, S.M. (1977). A shift of the mean level in a
sequence of independent normal random variable –a Bayesian approach.
Technometrics, 19, p. 503-506.
Menzefricke, U. (1981). A Bayesian analysis of a change in the precision of a
sequence of independent normal random variables at an unknown time point,
Journal of the Royal Statistical Society-C, 30, p. 141-146.
Page, E.S (1950). On problems in which change in a parameter is occurring at
an unknown time point. Biometrika, 37, p. 258-262.
Quandt, R.E. and J.B. Ramsey (1978). Estimating mixtures of normal
distributions and switching regressions, Journal of the American Statistical
Association, 73, p. 730-752.
Salazar, D. (1982). Structural changes in time series models, Journal of
Econometrics, 19, p. 147-163.
Silvey, S.D. (1958). The Lindisfarne scribes problem. Journal of the Royal
Statistical Society-B, 20, p. 93-101.
Smith, A.F.M. (1975). A Bayesian approach to inference about change point in
a sequence of random variables, Biometrika, 62, p. 407-416.
Venkatesan, D. and Arumugam, P. (2005). Structural changes in AR(1)
models: a Bayesian mixture approach, Bulletin of Pure and Applied Sciences,
Vol. 24E, p. 393-397.
Venkatesan, D. and Arumugam, P. (2007). Bayesian analysis of structural
changes in autoregressive models, American Journal of Mathematical and
Management Science, 27, No.1&2, p. 153-162.
Venkatesan, D., Arumugam, P., Vijayakumar, M. and Gallo, M. (2009).
Bayesian analysis of change point problem in autoregressive model: a
mixture model approach, Statistica and Applications, Vol. 11(2), p. 223-230.
