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Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends

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  • Mynbaev, Kairat

Abstract

We propose a general method of modeling deterministic trends for autoregressions. The method relies on the notion of $L_2$-approximable regressors previously developed by the author. Some facts from the theory of functions play an important role in the proof. In its present form, the method encompasses slowly growing regressors, such as logarithmic trends, and leaves open the case of polynomial trends.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:18448
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    References listed on IDEAS

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    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. 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.
    3. Rahbek, Anders & Christian Kongsted, Hans & Jorgensen, Clara, 1999. "Trend stationarity in the I(2) cointegration model," Journal of Econometrics, Elsevier, vol. 90(2), pages 265-289, June.
    4. Nabeya, Seiji, 2000. "Asymptotic Distributions For Unit Root Test Statistics In Nearly Integrated Seasonal Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 16(2), pages 200-230, April.
    5. 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.
    6. Serena Ng & Timothy J. Vogelsang, 2002. "Forecasting autoregressive time series in the presence of deterministic components," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 196-224, June.
    7. 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.
    8. Wing‐kuen Tam & Gregory Reinsel, 1998. "Seasonal Moving‐average Unit Root Tests in the Presence of a Linear Trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 609-625, September.
    9. 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.
    10. Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany.
    11. 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.
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    Cited by:

    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. Mynbayev, Kairat, 2007. "OLS Asymptotics for Vector Autoregressions with Deterministic Regressors," MPRA Paper 101688, University Library of Munich, Germany, revised 2018.
    3. 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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    More about this item

    Keywords

    autoregression; deterministic trend; OLS estimator asymptotics;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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