Test for Parameter Changes in the AR(1) Process

  • Kim, Soo-Hwa (Samsung Data Systems Co. Ltd., Seoul, 120-020) ;
  • Cho, Sin-Sup (Department of Statistics, Seoul Naitonal University, Seoul, 151-742, Korea. sinsup@stats.snu.ac.kr) ;
  • Park, Young J. (Department of Statistics, North Carolina State University, Raleigh, USA)
  • 발행 : 1997.09.01

초록

In this paper the parameter change problem in the stationary time series is considered. We propose a cumulative sum (CUSUM) of squares-type test statistic for detection of parameter changes in the AR(1) process. The proposed test statistic is based on the CUSIM of the squared observations and is shown to converge to a standard Brownian bridge. Simulations are performed to evaluate the performance of the proposed statistic and a real example is provided to illustrate the procedure.

키워드

참고문헌

  1. Journal of Time Series Analysis v.14 On the partial sums of residuals in autoregressive and moving average models Bai, J.
  2. Time Series Analysis : Theory and Practice 7 Baufays, P.;Rasson, J. P.
  3. Convergence of probability measures Billingsley, P.
  4. Time Series Analysis: Forecasting and Control(2nd ed.) Box, G.E.P.;Jenkins, G.M.
  5. Technometrics v.21 Robust methods for detection of shifts of the innovation variance of a time series Davis, R. A.
  6. Annals of Statistics v.23 Testing for a change in the parameter values and order of an autoregressive model Davis, R. A.;Huang, D.;Yao, Y. C.
  7. Journal of the American Statistical Association v.89 Use of cumulative sums of squares for retrospective detection of changes of variance Inclan, C.;Tiao, G.
  8. Journal of the Japan Statistical Society v.18 An estimation procedure in a non-stationary autoregressive model Kwoun, G. H.
  9. Journal of the American Statistical Association v.88 Bayesian inference and prediction for mean and variance shifts in autoregressive time series McCulloch, R. E.;Tsay, R. S.
  10. Zeit Wahrscheinlichkeitstheorie verweit Gebiete v.32 Invariance principles for dependent variables McLeish, D. L.
  11. Lecture Notes in statistics 11 Random Coefficient Autoregressive Models: An Introduction Nicholls, D. F.;Quinn, B. G.
  12. Journal of the Korean Applied Statistics v.1 A detection procedure for variance change in AR(1) model Ryu, G. Y.;Cho, S. S.
  13. Journal of Time Series Analysis v.7 Some doubly stochastic time series models TjΦstheim, D.
  14. Journal of Forecasting v.7 Outliers, level shifts, and variance changes in time series Tsay, R. S.
  15. Applied Statistics v.37 An autoregressive model with suddenly changing parameters and an application to stock market prices Tyssedal, J. S.;TjΦstheim, D.
  16. Applied Statistics v.25 Changes of variance in first-order autoregressive time series models-with an application Wichern, D. W.;Miller, R. B.;Hsu, D. A.