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Strictly stationary solutions of autoregressive moving average equations

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  • Peter J. Brockwell
  • Alexander Lindner

Abstract

Necessary and sufficient conditions for the existence of a strictly stationary solution of the equations defining an autoregressive moving average process driven by an independent and identically distributed noise sequence are determined. No moment assumptions on the driving noise sequence are made. Copyright 2010, Oxford University Press.

Suggested Citation

  • Peter J. Brockwell & Alexander Lindner, 2010. "Strictly stationary solutions of autoregressive moving average equations," Biometrika, Biometrika Trust, vol. 97(3), pages 765-772.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:3:p:765-772
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    File URL: http://hdl.handle.net/10.1093/biomet/asq034
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    Cited by:

    1. Spangenberg, Felix, 2013. "Strictly stationary solutions of ARMA equations in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 127-138.
    2. Tanujit Chakraborty & Ashis Kumar Chakraborty & Munmun Biswas & Sayak Banerjee & Shramana Bhattacharya, 2021. "Unemployment Rate Forecasting: A Hybrid Approach," Computational Economics, Springer;Society for Computational Economics, vol. 57(1), pages 183-201, January.
    3. P. Brockwell, 2014. "Recent results in the theory and applications of CARMA processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(4), pages 647-685, August.
    4. Peter J. Brockwell & Alexander Lindner, 2021. "Aspects of non‐causal and non‐invertible CARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 777-790, September.
    5. Ernst, Philip A. & Brown, Lawrence D. & Shepp, Larry & Wolpert, Robert L., 2017. "Stationary Gaussian Markov processes as limits of stationary autoregressive time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 180-186.
    6. Brandes, Dirk-Philip & Lindner, Alexander, 2014. "Non-causal strictly stationary solutions of random recurrence equations," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 113-118.
    7. Peter Brockwell & Alexander Lindner & Bernd Vollenbröker, 2012. "Strictly stationary solutions of multivariate ARMA equations with i.i.d. noise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1089-1119, December.
    8. Yining Chen, 2015. "Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 1-31, March.
    9. Martin Drapatz, 2016. "Strictly stationary solutions of spatial ARMA equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 385-412, April.
    10. Chao Zhang & Piotr Kokoszka & Alexander Petersen, 2022. "Wasserstein autoregressive models for density time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(1), pages 30-52, January.

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