A Study on the Least Squared Estimator of Autoregressive Models when Consecutive Missing Observations Exist

  • Ryu, Gui-Yeol (Department of Applied Statistics, Seo Kyeong University, Chongnung-Dong)
  • Published : 1996.12.01

Abstract

The properties of the residuals are investigated when K-consecutive observations are interpolated. The central limit theorem is also proved for the LSE for autoregressive parameters when $\kappa4--consecutive observations are contaminated. The performance of the interpolated LSE in small samples is investigated by simulation. And the interpolated with the Yule-Walker type estimator.

Keywords

References

  1. Communications in Statistics, Theory and Methods v.A no.10 Missing observatons in time series Abraham, B.
  2. The Annals of Statistics v.13 Estimation, filtering, and smoothing in state space models with incompletely specified initial conditions Ansley, C.F.;Kohn, R.
  3. Time Series Analysis : forecasting and control(2nd ed.) Box, G.E.P.;Jenkins,G.
  4. Applied Statistics v.25 Interpolating time series with applicatin to the estimation of holiday effects on electricity demand Brubacher, S.R.;Wilson, G.T.
  5. Journal of the Royal Statistical Society, Ser. B. v.51 leave-k-out diagnostics for time series (with discussion) Bruce, A.G.;Martin, R. D.
  6. Journal of the Korean Statistical Society v.22 Outlier Detextion Diagnostic based on Interpolation Method in Autoregressive Models Cho, S.;Ryu, G. Y.;Park, B.U.;Lee, J.J.
  7. Sankhya A v.43 Asymptotic theory for time series containing missing and amplitude modulated observations Dunsmuir, W.;Robinson, P. M.
  8. Journal of the American Statistical Association v.76 Estimation of time series models in the presence of missing data Dunsmuir, W.;Robinson, P.M.
  9. Introduction to Statistical Time Series Fuller, W. A.
  10. Statistical Analysis of Stationary Time Series Grenander, U.;Rosenblatt, M.
  11. Journal of the American Statistical Association v.79 Estimating missing observations in economic time series Harvey, A.C.;Pierse, R. G.
  12. Continuous univariate distributions-2 Johnson N. L.;Kotz S.
  13. Technometrics v.22 Maximum like lihood fitting of ARMA models to time series with missing observations Jones, R. H.
  14. Journal of the American Statistical Association v.81 Estimation, Prediction, and Interpolation for ARIMA Models With Missing Data Kohn, R.;Ansley, C.F.
  15. Unpublished Ph.D. dissertation, University of Wisconsin, Department of Statistics A Study on Influential Obervations in Linear Regression and Time Series Lee, J.J.
  16. Statistical Analysis with Missing Data Little, R.;Rubin, D.
  17. ASA Proceedings of the Business and Economic Statistics Section Outliers and Missing Observation in Time Series Ljung, G.M.
  18. Proceedings of time series analysis of irreguraly observed data A strategy to complete a time series with missing observations Miller, R.B.;Ferreiro;Parzen, E.(ed.)
  19. Biometrica v.61 The exact likelihod function for a mixed autoregressive-moving average process Newbold, P.
  20. Sankhy a Ser. A v.25 On spectral analysis with missing observation and amplitude modulation Parzen, E.
  21. The American Statistician v.45 A Note on Likelihood Estimation of Missing Values in Time Series Pe na, D.;Tiao, G. C.
  22. Journal of Time Series Analysis v.10 Estimation and interpolation of missing values of stationary time series Pourahmadi, M.
  23. Biometrika v.74 Asymtotic distribution of parameter estimators for onoconsecutively observed time series Reinsel, G.C.;Wincek, M. A.
  24. Unpublished Ph.D. dissertation, Seoul National University, Department of Computer Science and Statistics Outlier Detection Diagnostic in Time Series Ryu, G.Y.
  25. Time Series Analysis Wei, W.S.
  26. Biometrika v.74 Asymtotic distribution of parameter estimatiors for nonconsecutively observed time series Reinsel G.C.;Wincek M.A.
  27. Unpublished Ph.D.Dissertation, Seoul National University, Department of Computer Science and Statistics Outlier Detection Diagnostic in Time Seies Ryu,G.Y.
  28. Time Series Analysis Wei,W.S.