Mynbayev, Kairat (2007): OLS Asymptotics for Vector Autoregressions with Deterministic Regressors. Published in: EURASIAN MATHEMATICAL JOURNAL , Vol. 9, No. 1 (2018): pp. 4068.

PDF
MPRA_paper_101688.pdf Download (301kB)  Preview 
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 secondorder 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.
Item Type:  MPRA Paper 

Original Title:  OLS Asymptotics for Vector Autoregressions with Deterministic Regressors 
Language:  English 
Keywords:  timeseries regression, asymptotic distribution, OLS estimator, polynomial trend, deterministic regressor 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C00  General C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models 
Item ID:  101688 
Depositing User:  Kairat Mynbaev 
Date Deposited:  14 Jul 2020 13:09 
Last Modified:  14 Jul 2020 13:09 
References:  [1] T.W. Anderson, The Statistical Analysis of Time Series, Wiley & Sons, 1971. [2] T. Amemiya, Advanced Econometrics, Oxford, Blackwell, 1985. [3] T.W. Anderson, N. Kunitomo, Asymptotic distribution of regression and autoregression coefficients with martingale difference disturbances, J. Multivariate Anal. 40 (1992), 221–243. [4] T.W. Anderson, N. Kunitomo, Asymptotic robustness of tests of overidentification and predeterminedness, J. Econometrics. 62 (1994), 383–414. [5] D.W.K. Andrews, Laws of large numbers for dependent nonidentically distributed random variables, Economet. Theory. 4 (1988), 458–467. [6] D.W.K. Andrews, C.J. McDermott, Nonlinear econometric models with deterministically trending variables, Rev. Econ. Stud. 62 (1995), 343–360. [7] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, Cambridge University Press, 1987. [8] D.L. Burkholder, Distribution function inequalities for martingales, Ann. Prob. 1 (1973), 14–42. [9] W. Charemza, D.F. Deadman, New Directions in Econometric Practice: General to Specific Modelling, Cointegration, and Vector Autoregression, E. Elgar, 1992. [10] J. Davidson, Stochastic Limit Theory: An Introduction for Econometricians, Oxford University Press, 1994. [11] A. Dvoretzky, Asymptotic normality for sums of dependent variables, Proceedings of the Sixth Berkeley Symposium in Mathematical Statistics and Probability, University of California Press, 1972, 513–555. [12] F.R. Gantmacher, Matrizentheorie, VEB Deutscher Verlag der Wissenschaften, 1986. [13] P. Hall, C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, 1980. [14] J.D. Hamilton, Time Series Analysis, Princeton University Press, 1994. [15] T.H. Kim, S. Pfaffenzeller, T. Rayher, P. Newbold, Testing for linear trend with applications to relative commodity prices, J. Time Ser. Anal. 24 (2003), 539–551. [16] H. L¨utkepohl, Introduction to Multiple Time Series Analysis, SpringerVerlag, 1991. [17] K.T. Mynbaev, Lpapproximable sequences of vectors and limit distribution of quadratic forms of random variables, Adv. Appl. Math. 26 (2001), 302–329. [18] K.T. Mynbaev, Asymptotic properties of OLS estimates in autoregressions with bounded or slowly growing deterministic trends, Commun. Stat. Theory. 35 (2006), 499–520. [19] K.T. Mynbaev, Shortmemory linear processes and econometric applications, Wiley & Sons, 2011. [20] K.T. Mynbaev, Central limit theorems for weighted sums of linear processes: Lpapproximability versus Brownian motion, Economet. Theory, 25 (2009), 748763. [21] K.T. Mynbaev, A. Ullah, Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model, J. Multivariate Anal. 99 (2008), 245–277. [22] K.T. Mynbaev, Asymptotic distribution of the OLS estimator for a mixed regressive, spatial autoregressive model, J. Multivariate Anal. 101 (2010), 733–748. [23] K.T. Mynbaev, I. Castelar, The Strengths and Weaknesses of L2approximable Regressors. Two Essays on Econometrics, Fortaleza: Express˜ao Gr´afica. 1, 2001. http://mpra.ub.unimuenchen.de/9056/ [24] B. Nielsen, Strong consistency results for Least Squares estimators in general vector autoregressions with deterministic terms, Economet. Theory. 21 (2005), 534–561. [25] P.C.B. Phillips, Regression with slowly varying regressors and nonlinear trends, Economet. Theory. 23 (2007), 557614. [26] B.M. P¨otscher, I.R. Prucha, Basic structure of the asymptotic theory in dynamic nonlinear econometric models, Part I: Consistency and approximation concepts, Econometric Rev. 10 (1991), 125–216. [27] C.A. Sims, J.H. Stock, M.W. Watson, Inference in linear time series models with some unit roots, Econometrica. 58 (1990), 113–144. [28] K. Tanaka, Time Series Analysis: Nonstationary and Noninvertible Distribution Theory, Wiley & Sons, 1996. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/101688 