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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.

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File URL: http://mpra.ub.uni-muenchen.de/18448/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 18448.

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Date of creation: 2003
Date of revision: 2005
Handle: RePEc:pra:mprapa:18448

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Related research

Keywords: autoregression; deterministic trend; OLS estimator asymptotics;

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References

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  1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, Octomber.
  2. Nabeya, Seiji, 2000. "Asymptotic Distributions For Unit Root Test Statistics In Nearly Integrated Seasonal Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 16(02), pages 200-230, April.
  3. Clara Jørgensen & Hans Christian Kongsted & Anders Rahbek, 1996. "Trend-Stationarity in the I(2) Cointegration Model," Discussion Papers 96-12, University of Copenhagen. Department of Economics.
  4. Ng, Serena & Vogelsang, Tim, 2000. "Forecasting Autoregressive Time Series in the Presence of Deterministic Components," Working Papers 00-07, Cornell University, Center for Analytic Economics.
  5. Donald W.K. Andrews & C. John McDermott, 1993. "Nonlinear Econometric Models with Deterministically Trending Variables," Cowles Foundation Discussion Papers 1053, Cowles Foundation for Research in Economics, Yale University.
  6. Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany.
  7. 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 113-44, January.
  8. 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.
  9. 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.
  10. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
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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. 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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