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[The random walk model with autoregressive errors]
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.
|Date of creation:||2005|
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- 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.
- 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.
- Antonio Spilimbergo & Athanasios Vamvakidis, 2000.
"Real Effective Exchange Rate and the Constant Elasticity of Substitution Assumption,"
IMF Working Papers
00/128, International Monetary Fund.
- Spilimbergo, Antonio & Vamvakidis, Athanasios, 2003. "Real effective exchange rate and the constant elasticity of substitution assumption," Journal of International Economics, Elsevier, vol. 60(2), pages 337-354, August.
- 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.
- 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.
- 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.
- Kramer, Walter, 1998.
"Fractional integration and the augmented Dickey-Fuller Test,"
Elsevier, vol. 61(3), pages 269-272, December.
- Krämer, Walter, 1997. "Fractional integration and the augmented dickey-fuller test," Technical Reports 1997,06, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- Zhije Xiao & Peter C.B. Phillips, 1998.
"An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy,"
Royal Economic Society, vol. 1(RegularPa), pages 27-43.
- 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.
- 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.
- Zivot, Eric & Andrews, Donald W K, 2002.
"Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 25-44, January.
- Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
- 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.
- 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.
- 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, Universite de Montreal, Departement de sciences economiques.
- Vogelsang, Timothy J & Perron, Pierre, 1998. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1073-1100, November.
- 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.
- 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.
- Vogelsang, T.I. & Perron, P., 1991. "Nonstationary and Level Shifts With An Application To Purchasing Power Parity," Papers 359, Princeton, Department of Economics - Econometric Research Program.
- 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.
- 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.
- Banerjee, Anindya & Lumsdaine, Robin L & Stock, James H, 1992. "Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 271-87, July.
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