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The Finite-Sample E ects of VAR Dimensions on OLS Bias, OLS Variance, and Minimum MSE Estimators

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  • Steve Lawford

    ()
    (ENAC, France, University of Nottingham, UK, Philips College, Cyprus and The Rimini The Rimini Center for Economic Analysis, Italy)

  • Michalis P. Stamatogiannis

Abstract

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the nite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary rst-order VAR. Speci cally, we use Monte Carlo simulation and numerical optimization to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct speci cation and several types of over-parameterization of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain minimum mean squared error (MSE). Our results improve and extend one of the main nite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis (Econometrica 67 (1999) 163), generalize the univariate variance and MSE ndings of Abadir (Economics Letters 47 (1995) 263) to the multivariate setting, and complement various asymptotic studies.

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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 13-08.

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Date of creation: Jan 2008
Date of revision: Jan 2008
Handle: RePEc:rim:rimwps:13-08

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Keywords: Finite-sample bias; Monte Carlo simulation; nonstationary time series; response surfaces; vector autoregression.;

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  1. David Hendry & Hans-Martin Krolzig, 2003. "The Properties of Automatic Gets Modelling," Economics Series Working Papers 2003-W14, University of Oxford, Department of Economics.
  2. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-76, April.
  3. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
  4. Mackinnon, J.G. & Haug, A.A. & Michelis, L., 1996. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," G.R.E.Q.A.M. 96a09, Universite Aix-Marseille III.
  5. Karim Abadir & Kaddour Hadri & Elias Tzavalis, . "The Influence of VAR Dimensions on Estimator Biases," Discussion Papers 96/14, Department of Economics, University of York.
  6. Pere, Pekka, 2000. "Adjusted estimates and Wald statistics for the AR(1) model with constant," Journal of Econometrics, Elsevier, vol. 98(2), pages 335-363, October.
  7. Campos, Julia, 1986. "Finite-sample properties of the instrumental-variables estimator for dynamic simultaneous-equation subsystems with ARMA disturbances," Journal of Econometrics, Elsevier, vol. 32(3), pages 333-366, August.
  8. Ericsson, Neil R, 1991. "Monte Carlo Methodology and the Finite Sample Properties of Instrumental Variables Statistics for Testing Nested and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 59(5), pages 1249-77, September.
  9. Abadir, Karim M. & Larsson, Rolf, 2001. "The Joint Moment Generating Function Of Quadratic Forms In Multivariate Autoregressive Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 222-246, February.
  10. Jan F. Kiviet & Garry D. A. Phillips, 2005. "Moment approximation for least-squares estimators in dynamic regression models with a unit root *," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 115-142, 07.
  11. Vinod, H.D. & Shenton, L.R., 1996. "Exact Moments for Autor1egressive and Random walk Models for a Zero or Stationary Initial Value," Econometric Theory, Cambridge University Press, vol. 12(03), pages 481-499, August.
  12. Neil R. Ericsson & James G. MacKinnon, 1999. "Distributions of error correction tests for cointegration," International Finance Discussion Papers 655, Board of Governors of the Federal Reserve System (U.S.).
  13. James G. MacKinnon & Anthony A. Smith Jr., 1995. "Approximate Bias Correction in Econometrics," Working Papers 919, Queen's University, Department of Economics.
  14. Peter C.B. Phillips, 1985. "Asymptotic Expansions in Nonstationary Vector Autoregressions," Cowles Foundation Discussion Papers 765, Cowles Foundation for Research in Economics, Yale University.
  15. Abadir, Karim M., 1995. "Unbiased estimation as a solution to testing for random walks," Economics Letters, Elsevier, vol. 47(3-4), pages 263-268, March.
  16. Roy, Anindya & Fuller, Wayne A, 2001. "Estimation for Autoregressive Time Series with a Root Near 1," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 482-93, October.
  17. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-18, Nov.-Dec..
  18. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  19. Alain Breton & Dinh Pham, 1989. "On the bias of the least squares estimator for the first order autoregressive process," Annals of the Institute of Statistical Mathematics, Springer, vol. 41(3), pages 555-563, September.
  20. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-80, July.
  21. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier.
  22. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
  23. Nankervis, J. C. & Savin, N. E., 1988. "The exact moments of the least-squares estimator for the autoregressive model corrections and extensions," Journal of Econometrics, Elsevier, vol. 37(3), pages 381-388, March.
  24. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  25. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 1," Cowles Foundation Discussion Papers 811R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1987.
  26. Tanizaki, Hisashi, 2000. "Bias correction of OLSE in the regression model with lagged dependent variables," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 495-511, October.
  27. Abadir, Karim M., 1993. "Ols Bias in a Nonstationary Autoregression," Econometric Theory, Cambridge University Press, vol. 9(01), pages 81-93, January.
  28. Abadir, Karim M & Hadri, Kaddour, 2000. "Is More Information a Good Thing? Bias Nonmonotonicity in Stochastic Difference Equations," Bulletin of Economic Research, Wiley Blackwell, vol. 52(2), pages 91-100, April.
  29. Robert F. Engle & David F. Hendry & David Trumble, 1985. "Small-Sample Properties of ARCH Estimators and Tests," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 66-93, February.
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