Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Testing for a Unit Root in an ARIMA(p,1,q) Signal Observed with Measurement Error

  • Lee, Jong-Hyup (Department of Statistics, Sungshin Women's University, Seoul 136-742) ;
  • Shin, Dong-Wan (Department of Statistics, Ewha Womans University, Seoul 120-750)
  • Published : 1995.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

An ARIMA signal observed with measurement error is shown to have another ARIMA representation with nonlinear restrictions on parameters. For this model, the restricted Newton-Raphson estimator(RNRE) of the unit root is shown to have the same limiting distribution as the ordinary least squares estimator of the unit root in an AR(1) model tabulated by Dickey and Fuller (1979). The RNRE of parameters of the ARIMA(p,1,k) process and unit root tests base on the RNRE are developed.

Keywords

References

  1. Time Series - Theory and Methods Brockwell,P.J.;Davis,R.A.
  2. Annals of Statistics v.16 Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Process Chan,N.H.;Wei,C.Z.
  3. Journal of the American Statistical Association v.74 Distribution of the Estimators for Autoregressive Time Series with a Unit Root Dickey,D.A.;Fuller,W.A.
  4. Introduction to Statistical Time Series Fuller,W.A.
  5. Biometrika v.76 Testing for a Unit Root in the Presence of Moving Average Errors Hall,A.
  6. Annals of Statistics v.2 Estimation of Models of Autoregressive Signal Plus White Noise Pagano,M.
  7. Journal of Econometrics v.48 Testing for Unit Roots in Autoregressive Moving Average Models. An Instrumental Variable Approach Pantular,S.G.;Hall,A.
  8. Econometrica v.55 Time Series Regression with a Unit Root Phillips,P.C.B.
  9. Biometrika v.75 Testing for a Unit Root in Time Series Regression Phillips,P.C.B.;Perron,P.
  10. Journal of the American Statistical Association v.80 Hypothesis Testing in ARIMA(p, 1, q) Models Said,S.E.;Dickey,D.A.
  11. International Journal of Control v.30 Recursive Parameter Estimation of an Autoregressive Process Disturbed by White Noise Sakai,H.;Arase,M.
  12. Journal of the Time Series Analysis v.14 Maximum Likelihood Estimation for Autoregressive Process Disturbed by a Moving Average Shin,D.W.
  13. Statistics & Probability Letters v.18 A Note on Testing for a Unit Root in an ARIMA(p, 1, 0) Signal Observed with MA(q) Noise Shin,D.;Sarkar,S.
  14. Communications in Statistics - Theory and Methods v.23 no.9 Testing for a Unit Root in an ARIMA(p, 1, 0) Signal Observed with MA(q) Noise Shin,D.W.;Sarkar,S.
  15. SIAM Journal of Numerical Analysis v.6 Factorization of the Covariance Generating Function of a Pure Moving Average Process Wilson,G.
  16. Journal of the Time Series Analysis v.16 Results on Estimation and Testing for a Unit Root in the Nonstationary Autoregressive Moving-Average Model Yap,S.F.;Reinsel,G.C.