Journal of the Korean Statistical Society

  • 제29권3호
  • /
  • Pages.351-360
  • /
  • 2000
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

The Cusum of Squares Test for Variance Changes in Infinite Order Autoregressive Models

  • Park, Siyun (Department of Statistics, Seoul National University, Seoul, 151-742) ;
  • Lee, Sangyeol (Department of Statistics, Seoul National University, Seoul, 151-742) ;
  • Jongwoo Jeon (Department of Statistics, Seoul National University, Seoul, 151-742)
  • 발행 : 2000.09.01
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초록

This paper considers the problem of testing a variance change in infinite order autoregressive models. A cusum of squares test based on the residuals from an AR(q) model is constructed analogous to Inclan and Tiao (1994)'s test statistic, where q is a sequence of positive integers diverging to $\infty$. It is shown that under regularity conditions the limiting distribution of the test statistic is the sup of a standard Brownian bridge. Simulation results are given to illustrate the performance of the test.

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참고문헌

  1. Metrika v.31 Inference about the parameters of a time series model with changing variance Abraham, B.;Wei, W.W.S.
  2. In Time Series Analysis: Theory and Pracrice. 7 Variance changes in autoregressive models Baufay, P.;Rasson, J.P.;O.D. Anderson(ed)
  3. Time Series: Theory and Methods Brockwell, P.J.;Daving, R.A.
  4. J. Roy. Statist. Soc. B v.37 Techniques for testing the constancy of regression relationsphips over time Brown, R.L.;Durbin, J.;Evans, J.M.
  5. Limit Theorems in Change Point Analysis Csorgo, M.;Horvath, L.
  6. Appl. Statist. v.26 Tests for variance shift at an unknown time point Hsu, D.A.
  7. J. Amer. Statist. Assoc. v.69 On the stable paretian behavior of stock-market prices Hsu, D.A.;Miller, R.B.;Wichern, D.W.
  8. J. Amer. Statist. Assoc. v.89 Use of cumulative sums of squares for retrospective detection of changes of variances Inclan, C.;Tiao, G.C.
  9. To appear in Communications in Statistics: Theory and Methods On the cusum test for parameter changes in GARCH(1,1) models Kim, S.;Cho, S.;Lee, S.
  10. Ann. Statist v.27 On residual empirical processes of stochastic regression models with applications to time series Lee, S.;Wei, C.Z.
  11. Submitted for publication The cusum of squares test for scale changes in infinite order moving average processes Lee, S.;Park, S.
  12. Ann. Statist v.8 Asymptotically efficient selection of the order for estimating parametrs of linear process Shibata, R.
  13. Ann. Statist v.21 The effect of serial corrlelation on tests for parameter change at unknown time Tang, S.M.;MacNeil, I.B.
  14. J. Forecasting v.7 Outliers, level shifts, and variance change in time series Tsay, R.S.
  15. Appl. Statist v.25 Chagnes of variance in first-order autoregressive time series models with an application Wichern, D.W.;Miller, R.B.;Hsu, D.A.