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OLS Asymptotics for Vector Autoregressions with Deterministic Regressors

Author

Listed:
  • Mynbayev, Kairat
Abstract
We consider a mixed vector autoregressive model with deterministic exogenous regressors and an autoregressive matrix that has characteristic roots inside the unit circle. The errors are (2+\epsilon)-integrable martingale differences with heterogeneous second-order conditional moments. The behavior of the ordinary least squares (OLS) estimator depends on the rate of growth of the exogenous regressors. For bounded or slowly growing regressors we prove asymptotic normality. In case of quickly growing regressors (e.g., polynomial trends) the result is negative: the OLS asymptotics cannot be derived using the conventional scheme and any diagonal normalizer.

Suggested Citation

  • Mynbayev, Kairat, 2007. "OLS Asymptotics for Vector Autoregressions with Deterministic Regressors," MPRA Paper 101688, University Library of Munich, Germany, revised 2018.
    • Handle: RePEc:pra:mprapa:101688
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    References listed on IDEAS

    as
    1. Mynbaev, Kairat T., 2010. "Asymptotic distribution of the OLS estimator for a mixed spatial model," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 733-748, March.
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    6. Mynbaev, Kairat T., 2009. "Central Limit Theorems For Weighted Sums Of Linear Processes: Lp -Approximability Versus Brownian Motion," Econometric Theory, Cambridge University Press, vol. 25(3), pages 748-763, June.
    7. Mynbaev, Kairat, 2000. "$L_p$-Approximable sequences of vectors and limit distribution of quadratic forms of random variables," MPRA Paper 18447, University Library of Munich, Germany, revised 2001.
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    9. Mynbaev, Kairat, 2006. "Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model," MPRA Paper 4411, University Library of Munich, Germany.
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    12. Mynbaev, Kairat T. & Ullah, Aman, 2008. "Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 245-277, February.
    13. Anderson, T. W. & Kunitomo, Naoto, 1994. "Asymptotic robustness of tests of overidentification and predeterminedness," Journal of Econometrics, Elsevier, vol. 62(2), pages 383-414, June.
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    15. Wojciech W. Charemza & Derek F. Deadman, 1992. "New Directions In Econometric Practice," Books, Edward Elgar Publishing, number 84.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    time-series regression; asymptotic distribution; OLS estimator; polynomial trend; deterministic regressor;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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