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Model identification for infinite variance autoregressive processes


  • Andrews, Beth
  • Davis, Richard A.


We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside the unit circle in the complex plane). We examine the performance of the order selection procedures for finite samples via simulation, and use the techniques to fit a noncausal autoregressive model to stock market trading volume data.

Suggested Citation

  • Andrews, Beth & Davis, Richard A., 2013. "Model identification for infinite variance autoregressive processes," Journal of Econometrics, Elsevier, vol. 172(2), pages 222-234.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:222-234 DOI: 10.1016/j.jeconom.2012.08.009

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    References listed on IDEAS

    1. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    2. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    3. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
    4. Gallagher, Colin M., 2001. "A method for fitting stable autoregressive models using the autocovariation function," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 381-390, July.
    5. Shiqing Ling, 2005. "Self-weighted least absolute deviation estimation for infinite variance autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 381-393.
    6. Breid, F. Jay & Davis, Richard A. & Lh, Keh-Shin & Rosenblatt, Murray, 1991. "Maximum likelihood estimation for noncausal autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 175-198, February.
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    Cited by:

    1. repec:eee:econom:v:200:y:2017:i:1:p:118-134 is not listed on IDEAS
    2. Fries, Sébastien & Zakoian, Jean-Michel, 2017. "Mixed Causal-Noncausal AR Processes and the Modelling of Explosive Bubbles," MPRA Paper 81345, University Library of Munich, Germany.
    3. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    4. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.

    More about this item


    Akaike’s information criterion; All-pass models; Autoregressive processes; Infinite variance; Noncausal;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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