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Moving-average representation of autoregressive approximations

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  • Bühlmann, Peter

Abstract

We study the properties of an MA([infinity])-representation of an autoregressive approximation for a stationary, real-valued process. In doing so we give an extension of Wiener's theorem in the deterministic approximation setup. When dealing with data, we can use this new key result to obtain insight into the structure of MA([infinity])-representations of fitted autoregressive models where the order increases with the sample size. In particular, we give a uniform bound for estimating the moving-average coefficients via autoregressive approximation being uniform over all integers.

Suggested Citation

  • Bühlmann, Peter, 1995. "Moving-average representation of autoregressive approximations," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 331-342, December.
    • Handle: RePEc:eee:spapps:v:60:y:1995:i:2:p:331-342
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    1. Dahlhaus, R. & Pötscher, B. M., 1989. "Convergence results for maximum likelihood type estimators in multivariable ARMA models II," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 241-244, August.
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    3. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    4. R. J. Bhansali, 1989. "Estimation Of The Moving‐Average Representation Of A Stationary Process By Autoregressive Model Fitting," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 215-232, May.
    5. Lutkepohl, Helmut, 1989. "A note on the asymptotic distribution of impulse response functions of estimated var models with orthogonal residuals," Journal of Econometrics, Elsevier, vol. 42(3), pages 371-376, November.
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    1. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    2. Rupasinghe, Maduka & Samaranayake, V.A., 2012. "Asymptotic properties of sieve bootstrap prediction intervals for FARIMA processes," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2108-2114.
    3. George Kapetanios & Zacharias Psaradakis, 2006. "Sieve Bootstrap for Strongly Dependent Stationary Processes," Working Papers 552, Queen Mary University of London, School of Economics and Finance.
    4. Patrick Marsh, "undated". "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
    5. Alonso, Andrés M. & Peña, Daniel & Romo, Juan, 2003. "On sieve bootstrap prediction intervals," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 13-20, October.

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