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[The random walk model with autoregressive errors]

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  • George, Halkos
  • Ilias, Kevork

Abstract

In this study we show that a random walk model with drift and first order autocorrelated errors, AR(1), behaves like an ARIMA(1,1,0). The last one is extracted from the unrestricted model of the Augmented Dickey Fuller test using as an explanatory variable a lag of order one difference of the series under consideration when H0 is true. Through Monte Carlo simulations we show that when the population model is a random walk with moderate AR(1) autocorrelation in the errors we have a high type II error either in small or large samples. Thus we are accepting as a population model the random walk with unfortunately uncorrelated errors. This causes problems at the stage of making predictions when constructing prediction intervals of the series we use 2 standard deviations of the forecast error above and below the predicted value. More specifically, the actual probability the prediction interval to include the real future value is really smaller than the nominal one of 95.44% even if the number of forecasting periods ahead is relatively small compared to the sample size we are using.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 33312.

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Date of creation: 2005
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Handle: RePEc:pra:mprapa:33312

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Keywords: Τυχαίος περίπατος με περιπλάνηση; ARIMA(1; 1; 0); Προβλέψεις;

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References

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  1. Eric Zivot & Donald W.K. Andrews, 1990. "Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Cowles Foundation Discussion Papers 944, Cowles Foundation for Research in Economics, Yale University.
  2. George Halkos & Ilias Kevork, 2005. "A comparison of alternative unit root tests," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(1), pages 45-60.
  3. Kim, Dongcheol & Kon, Stanley J., 1999. "Structural change and time dependence in models of stock returns," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 283-308, September.
  4. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-20, July.
  5. Antonio Spilimbergo & Athanasios Vamvakidis, 2000. "Real Effective Exchange Rate and the Constant Elasticity of Substitution Assumption," IMF Working Papers 00/128, International Monetary Fund.
  6. Stephen J. Leybourne & Paul Newbold, 1999. "The behaviour of Dickey-Fuller and Phillips-Perron tests under the alternative hypothesis," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 92-106.
  7. Krämer, Walter, 1997. "Fractional integration and the augmented dickey-fuller test," Technical Reports 1997,06, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  8. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Bisaglia, Luisa & Procidano, Isabella, 2002. "On the power of the Augmented Dickey-Fuller test against fractional alternatives using bootstrap," Economics Letters, Elsevier, vol. 77(3), pages 343-347, November.
  10. Zhijie Xiao & Peter C.B. Phillips, 1997. "An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the U.S. Economy," Cowles Foundation Discussion Papers 1161, Cowles Foundation for Research in Economics, Yale University.
  11. repec:wop:syecwp:2000-3 is not listed on IDEAS
  12. Prasad V. Bidarkota, 2000. "Asymmetries in the Conditional Mean Dynamics of Real GNP: Robust Evidence," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 153-157, February.
  13. Anindya Banerjee & Robin L. Lumsdaine & James H. Stock, 1990. "Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence," NBER Working Papers 3510, National Bureau of Economic Research, Inc.
  14. Hassler, Uwe & Wolters, Jurgen, 1994. "On the power of unit root tests against fractional alternatives," Economics Letters, Elsevier, vol. 45(1), pages 1-5, May.
  15. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  16. Sung Ahn & Stergios Fotopoulos & Lijian He, 2001. "Unit Root Tests With Infinite Variance Errors," Econometric Reviews, Taylor & Francis Journals, vol. 20(4), pages 461-483.
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