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Simple consistent estimation of the coefficients of a linear filter

Author

Listed:
  • Brockwell, P. J.
  • Davis, R. A.

Abstract

A simple procedure is proposed for estimating the coefficients {[psi]} from observations of the linear process X1=[summation operator]xJ=0[psi]JZ1-j, 1=1,2... The method is based on the representation of X1 in terms of the innovations, Xn-Xn, N=1,..., 1, where Xn is the best mean square predictor of Xn is span {X1,...X0-1}. The asymptotic distribution of the sequence of estimators is derived and its applications to inference for ARMA processes are discussed.

Suggested Citation

  • Brockwell, P. J. & Davis, R. A., 1988. "Simple consistent estimation of the coefficients of a linear filter," Stochastic Processes and their Applications, Elsevier, vol. 28(1), pages 47-59, April.
    • Handle: RePEc:eee:spapps:v:28:y:1988:i:1:p:47-59
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    Citations

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    Cited by:

    1. D. S. Poskitt, 2004. "On The Identification and Estimation of Partially Nonstationary ARMAX Systems," Monash Econometrics and Business Statistics Working Papers 20/04, Monash University, Department of Econometrics and Business Statistics.
    2. Vougas, Dimitrios V., 2008. "New exact ML estimation and inference for a Gaussian MA(1) process," Economics Letters, Elsevier, vol. 99(1), pages 172-176, April.
    3. Jirak, Moritz, 2014. "Simultaneous confidence bands for sequential autoregressive fitting," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 130-149.
    4. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    5. Anderson, Paul L. & Meerschaert, Mark M. & Vecchia, Aldo V., 1999. "Innovations algorithm for periodically stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 149-169, September.
    6. Anderson, Paul L. & Kavalieris, Laimonis & Meerschaert, Mark M., 2008. "Innovations algorithm asymptotics for periodically stationary time series with heavy tails," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 94-116, January.

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