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OLS Asymptotics for Vector Autoregressions with Deterministic Regressors

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  • 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

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    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.
    2. Tae‐Hwan Kim & Stephan Pfaffenzeller & Tony Rayner & Paul Newbold, 2003. "Testing for Linear Trend with Application to Relative Primary Commodity Prices," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 539-551, September.
    3. Donald W. K. Andrews & C. John McDermott, 1995. "Nonlinear Econometric Models with Deterministically Trending Variables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(3), pages 343-360.
    4. 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.
    5. Phillips, Peter C.B., 2007. "Regression With Slowly Varying Regressors And Nonlinear Trends," Econometric Theory, Cambridge University Press, vol. 23(4), pages 557-614, August.
    6. 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.
    7. 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.
    8. Nielsen, Bent, 2005. "Strong Consistency Results For Least Squares Estimators In General Vector Autoregressions With Deterministic Terms," Econometric Theory, Cambridge University Press, vol. 21(3), pages 534-561, June.
    9. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    10. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    11. 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.
    12. Anderson, T. W. & Kunitomo, Naoto, 1992. "Asymptotic distributions of regression and autoregression coefficients with martingale difference disturbances," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 221-243, February.
    13. Mynbaev, Kairat, 2006. "Asymptotic Distribution of the OLS Estimator for a Mixed Regressive, Spatial Autoregressive Model," MPRA Paper 4411, University Library of Munich, Germany.
    14. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    15. Mynbaev, Kairat, 2003. "Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends," MPRA Paper 18448, University Library of Munich, Germany, revised 2005.
    16. Wojciech W. Charemza & Derek F. Deadman, 1992. "New Directions In Econometric Practice," Books, Edward Elgar Publishing, number 84.
    17. Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany.
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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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