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On The Recursive Fitting Of Subset Autoregressions

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  • Jack H. W. Penm
  • R. D. Terrell

Abstract

. In fitting a vector autoregressive process which may include lags up to and including lag K, we may wish to search for the subset vector autoregressive process of size k (where k is the number of lags with non‐zero coefficient matrices, k= 1, 2, K) which has the minimum generalized residual variance. This paper provides a recursive procedure, which is initialized by evaluating all‘forwardand’‘backward’ autoregressions in which k= 1. The recursion then allows one to develop successively all subsets of size k= 2, k= 3 up to k=K. The optimum subset vector autoregression is found by employing the proposed recursive procedures in conjunction with model selection criteria. This approach is used on simulated data to assess its performance and to re‐examine the annual trappings of the Canadian lynx investigated by Tong (1977).

Suggested Citation

  • Jack H. W. Penm & R. D. Terrell, 1982. "On The Recursive Fitting Of Subset Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(1), pages 43-59, January.
    • Handle: RePEc:bla:jtsera:v:3:y:1982:i:1:p:43-59
    DOI: 10.1111/j.1467-9892.1982.tb00329.x
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    Cited by:

    1. Hsu, Nan-Jung & Hung, Hung-Lin & Chang, Ya-Mei, 2008. "Subset selection for vector autoregressive processes using Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3645-3657, March.
    2. repec:jss:jstsof:08:i05 is not listed on IDEAS
    3. Brockwell, Peter J. & Davis, Richard A. & Trindade, A. Alexandre, 2004. "Asymptotic properties of some subset vector autoregressive process estimators," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 327-347, August.
    4. Brockwell, P. J. & Dahlhaus, R., 2004. "Generalized Levinson-Durbin and Burg algorithms," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 129-149.
    5. Baillie, Richard T. & Cho, Dooyeon & Rho, Seunghwa, 2024. "Combining Long and Short Memory in Time Series Models: the Role of Asymptotic Correlations of the MLEs," Econometrics and Statistics, Elsevier, vol. 29(C), pages 88-112.
    6. Ayman A. Amin & Walid Emam & Yusra Tashkandy & Christophe Chesneau, 2023. "Bayesian Subset Selection of Seasonal Autoregressive Models," Mathematics, MDPI, vol. 11(13), pages 1-13, June.
    7. Hall, A.D, 1999. "Parametric forecasts of Australian yield curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 541-549.
    8. H. Glendinning, Richard, 2001. "Selecting sub-set autoregressions from outlier contaminated data," Computational Statistics & Data Analysis, Elsevier, vol. 36(2), pages 179-207, April.

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