George, Halkos and Ilias, Kevork (2005): Το υπόδειγμα τυχαίου περιπάτου με αυτοπαλίνδρομα σφάλματα.

PDF
MPRA_paper_33312.pdf Download (301Kb)  Preview 
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.
Item Type:  MPRA Paper 

Original Title:  Το υπόδειγμα τυχαίου περιπάτου με αυτοπαλίνδρομα σφάλματα 
English Title:  The random walk model with autoregressive errors 
Language:  Greek 
Keywords:  Τυχαίος περίπατος με περιπλάνηση; ARIMA(1,1,0); Προβλέψεις 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C50  General 
Item ID:  33312 
Depositing User:  G.E. Halkos 
Date Deposited:  11. Sep 2011 16:16 
Last Modified:  12. Feb 2013 20:40 
References:  Ahn, S.K., Fotopoulos, S.B., and He, L. (2001). “Unit root tests with infinite variance errors”. Econometric Review, 20, 461483 A.S.L. and Associates (1997). Sulfur Emissions By Country And Year, Report No: DE96014790, US Department of Energy, Washington DC. Banerjee, A., Lumsdaine, R., and Stock, J. (1992). “Recursive and sequential tests of the unit root and trend break hypothesis: Theory and international evidence”. Journal of Business and Economic Statistics, 10, 271287 Bidarkota, P.V. (2000). “Asymmetries in the conditional mean dynamics of real GNP: Robust evidence”. Review of Economics and Statistics, 82, 153157 Bisaglia L., and Procidano, I. (2002). “On the power of the Augmented DickeyFuller test against fractional alternatives bootstrap”. Economics Letters, 77, 343347 Box, G.E.P., and Muller, M.E. (1958). “A Note on the Generation of Random Normal Deviaties”. Ann. Math. Statist. 29: 610611 Chaudhuri, K. and Wu, Y. (2003). “Random walk versus breaking trend in stock prices: Evidence from emerging markets”. Journal of Banking and Finance, 27, 575592 Dickey, D.A., and Fuller, W.A. (1979). “Distribution of the Estimators for Autoregressive TimeSeries with Unit Root”. Journal of the American Statistical Association, 74, 427431 Dickey, D.A., and Fuller, W.A. (1981). “Likelihood Ratio Statistics for Autoregressive Time Series with a unit Root”. Econometrica, 49, 10571072 Elliot G., Rothenberg, T.J., and Stock, J.H. (1996). “Efficient tests for an autoregressive unit root”. Econometrica, 64, 813836 Fuller, W.A. (1996). Introduction to statistical Time Series, 2nd edn, Wiley, New York Gallegari F., Cappuccio N., and Lubian D. (2003). “Asymptotic inference in time series regressions with a unit root and infinite variance errors”. Journal of Statistical Planning and Inference, 116, 277303 Halkos G.E. and Kevork, I.S. (2003). A comparison of alternative unit root tests. Discussion Papers Series 0302, Department of Economics University of Thessaly Hassler, U. and Wolters, J. (1994). “On the power of unit root test against fractional alternatives”. Economics Letters, 45, 15 Kevork , I.S. (1990). Confidence Interval Methods for Discrete Event Computer Simulation: Theoretical Properties and Practical Recommendations. Unpublished Ph.D. Thesis, University of London, London Kim, D. and Kon, S.J. (1999). “Structural change and time dependence in models of stock returns”. Journal of Empirical Finance, 6, 283308 Krämer, W. (1998). “Fractional integration and the augmented Dickey Fuller test”. Economics Letters, 61, 269272 Law, A.M., and Kelton, W.D. (1982). Simulation Modelling and Analysis. McGrawHill, New York Lepohn, A. S., D.H. Janja and Rudolf, B.H. (1999). “Estimating historical anthropogenic global sulfur emission patterns for the period 18601990”, Atmospheric Environment, 33, 24352444 Levin, A. and Lin, C.F. (1993). Unit root test in panel data: asymptotic and finite sample properties. University of California at San Diego, Discussion Paper 92/93 Leybourne S., Newbold P. (1999). “The behaviour of Dickey Fuller and Phillips Perron under the alternative hypothesis”. Econometrics Journal, 2(1), 92106 Perron, P. (1989). “The great crash, the oil price shock and the unit root hypothesis”. Econometrica, 55, 277302 Perron P., and Vogelsang, T.J. (1992). “Nonstationary and level shifts with an application to purchasing power parity”. Journal of Business and Economic Statistics, 10, 301320. Pindyck, R.S., and Rubinfeld, D.L. (1998). Econometric Models and Economic Forecasts. 4th edn. McGrawHill International Editions Sanchez, I. (2003). “Efficient forecasting in nearly nonstationary processes”. Journal of Forecasting, in prepapration Shin D.W., and Lee, J.H. (2000). “Consistency of the maximum likelihood estimators for nonstationary ARMA regression with time trends”. Journal of Statistical Planning Inference, 87, 5568 Skin D.W., and Fuller, W.A. (1998). “Unit root tests based on unconditional maximum likelihood estimation for the autoregressive moving average”. Journal of Time Series Analysis, 19, 591599 Spilimbergo, A. and Vamvakidis, A. (2003). “Real effective exchange rate and the constant elasticity of substitution assumption”. Journal of International Economics, 60, 337354 Vogelsang, T.J. and Perron, P. (1998). Additional tests for a unit root allowing for a break in the trend function at an unknown time. International Economic Review, 39, 10731100 Xiao Z., and Phillips, P.C.B. (1998). “An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy”. Econometric Journal, 1, 2743 Zivot E., and Andrews, D.W.K. (1992). “Further evidence on the great crash, the oilprice shock, and the unitroot hypothesis”. Journal of Business and Economic Statistics, 10, 251270 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/33312 