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Sequential Analysis
Design Methods and Applications
Volume 30, 2011 - Issue 2
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Original Articles

On Asymptotic Normality of Sequential LS-Estimates of Unstable Autoregressive Processes

L. Galtchouk IRMA, Strasbourg University, Strasbourg, FranceCorrespondence[email protected]
&
V. Konev Department of Applied Mathematics and Cybernetics, Tomsk University, Tomsk, Russia
Pages 117-144 | Received 08 Dec 2008, Accepted 23 Dec 2010, Published online: 02 May 2011

REFERENCES

  • Ahtola , J. A. and Tiao , G. C. ( 1987 ). Distribution of Least Squares Estimators of Autoregressive Parameters for a Process with Complex Roots on the Unit Circle , Journal of Time Series Analysis 8 : 1 – 14 .
  • Anderson , T. W. ( 1971 ). The Statistical Analysis of Time Series , New York : Wiley .
  • Chan , N. H. and Wei , C. Z. ( 1988 ). Limiting Distribution of Least Squares Estimates of Unstable Autoregressive Processes , Annals of Statistics 16 : 367 – 401 .
  • Dickey , D. A. and Fuller , W. A. ( 1979 ). Distribution of the Estimators for Autoregressive Time Series with a Unit Root , Journal of American Statistical Association 74 : 427 – 431 .
  • Galtchouk , L. and Konev , V. V. ( 2003 ). On Uniform Asymptotic Normality of Sequential Least Squares Estimators for the Parameters in a Stable AR(1) , Sequential Analysis 22 : 31 – 54 .
  • Galtchouk , L. and Konev , V. V. ( 2004 ). On Uniform Asymptotic Normality of Sequential Least Squares Estimators for the Parameters in a Stable AR(p) , Journal of Multivariate Analysis 91 : 119 – 142 .
  • Galtchouk , L. and Konev , V. V. ( 2006 ). Sequential Estimation of the Parameters in Unstable AR(2) , Sequential Analysis 25 : 25 – 43 .
  • Galtchouk , L. and Konev , V. V. ( 2010 ). On Asymptotic Normality of Sequential LS-Estimate for Unstable Autoregressive Process AR(2) , Journal of Multivariate Analysis 101 : 2616 – 2636 .
  • Lai , T. L. and Siegmund , D. ( 1983 ). Fixed-Accuracy Estimation of an Autoregressive Parameter , Annals of Statistics 11 : 478 – 485 .
  • Lai , T. L. and Wei , C. Z. ( 1983 ). Asymptotic Properties of General Autoregressive Models and Strong Consistency of Least Squares Estimates of Their Parameters , Journal of Multivariate Analysis 13 : 1 – 23 .
  • Rao , M. M. ( 1978 ). Asymptotic Distribution of an Estimator of the Boundary Parameter of an Unstable Process , Annals of Statistics 6 : 185 – 190 .
  • Sriram , T. N. ( 1987 ). Sequential Estimation of the Mean of a First Order Stationary Autoregressive Process , Annals of Statistics 15 : 1079 – 1090 .
  • Sriram , T. N. ( 1988 ). Sequential Estimation of the Autoregressive Parameter in a First Order Autoregressive Process , Sequential Analysis 7 : 53 – 74 .
  • Varga , R. ( 2000 ). Matrix Iterative Analysis , Berlin : Springer .
  • White , J. S. ( 1958 ). The Limiting Distribution of the Serial Correlation Coefficient in the Explosive Case , Annals of Mathematical Statistics 29 : 1188 – 1197 .
  • Recommended by Sangyeol Lee

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