Halkos, George and Kevork, Ilias (2006): Forecasting an ARIMA (0,2,1) using the random walk model with drift.

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Abstract
In this paper we show that the random walk model with drift behaves like an ARIMA (0,2,1) when its parameter θ is greater but close to –1. Using the random walk for predicting future values of an ARIMA (0,2,1) process, we find out that when θ is not so close to –1, the performance of the prediction interval for the period forecast is not satisfactory. Particularly, for large, the achieved coverage, namely, the probability the prediction interval to include the future value is quite low. Even in the cases of large samples and small , although the random walk coverage approaches that of the ARIMA, the random walk produces wider prediction intervals. This picture changes when we forecast ARIMA (0,2,1) values for θ close to –1. The random walk should be preferred as it produces on average narrower confidence intervals, and its coverage is almost the same with the nominal coverage of the ARIMA (0,2,1).
Item Type:  MPRA Paper 

Original Title:  Forecasting an ARIMA (0,2,1) using the random walk model with drift 
Language:  English 
Keywords:  ARIMA; Random Walk; Monte Carlo Simulations 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models; Single Variables > C22  TimeSeries Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models 
Item ID:  31841 
Depositing User:  Nickolaos Tzeremes 
Date Deposited:  26. Jun 2011 10:24 
Last Modified:  28. Feb 2013 23:06 
References:  Abraham B. and Ledolter J. 1983. Statistical methods for forecasting, Wiley, New York. Ahn S.K., Fotopoulos S.B., He L. 2001. Unit root tests with infinite variance errors. Econometric Review 20: 461483 Andrews, D.K. 1993. Tests for parameter instability and structural change with unknown change point. Econometrica 59: 817858 A.S.L., Associates 1997. Sulfur Emissions By Country And Year, Report No: DE96014790, US Department of Energy, Washington DC. Banerjee A., Lumsdaine, R., 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 Bisaglia L., Procidano I. 2002. On the power of the Augmented DickeyFuller test against fractional alternatives bootstrap. Economics Letters 77: 343347 Box G.E.P., Jenkins, G.M. 1970. Time Series Analysis: Forecasting and Control. Holden Say, San Francisco (revised edition 1976) Box G.E.P., Jenkins G.M., Reinsel G.C. 1994. Time Series Analysis: Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs, NJ Brockwell P.J., Davis R.A. 2002. Introduction to Time Series and Forecasting, 2nd edn. Springer Chan N.H., Tran L.T. 1989. On the firstorder autoregressive process with infinite variance. Econometric Theory 5: 354362 Chiu C.C., Cook D.F., Pignatiello J.J. 1995. Radial basis function neural network for Kraft pulping forecasting. International Journal of Industrial Engineering 2(2): 209215 Cook D.F., Chiu C.C. 1997. Predicting the internal bond strength of particleboard utilizing a radial basis function neural network, Engineering Applications AI 10(2): 171177 Dickey D.A. 1976. Estimation and hypothesis testing for nonstationary time series. Ph.D Thesis, Iowa State University, Iowa Dickey D.A., Fuller W.A. 1976. Distribution of the estimators for autoregressive time series with a unit root. Journal of American Statistical Association 74: 427431 Dickey D.A., 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., Fuller W.A. 1981. Likelihood Ratio Statistics for Autoregressive Time Series with a unit Root. Econometrica, 49: 10571072 Elliot G., Rothenberg T.J., 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., 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 Gao X.M., Gao X.Z., Tanskanen J., Ovaska, S.J. 1997. Power prediction in mobile communications systems using an optimal neural network structure. IEEE Transportation Neural Networks 8(6), 14461455 Granger C.W.J., Joyeux R. 1980. An introduction to longmemory time series models and fractional differencing. Journal of Time Series Analysis, 1: 1539 Halkos G.E., Kevork I.S. (2003). A comparison of alternative unit root tests. Discussion Papers Series 0302, Department of Economics University of Thessaly Hassler, U., Wolters, J. 1994. On the power of unit root test against fractional alternatives. Economics Letters, 45: 15 Hosking J.R.M. 1981. Fractional differencing. Biometrika 68: 165176 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 Krämer W. 1998. Fractional integration and the augmented Dickey Fuller test. Economics Letters, 61: 269272 Lepohn, A.S., Janja D.H., Rudolf B.H. 1999. Estimating historical anthropogenic global sulfur emission patterns for the period 18601990, Atmospheric Environment, 33: 24352444 Leybourne S., Newbold P. 1999. The behaviour of Dickey Fuller and Phillips Perron under the alternative hypothesis. Econometrics Journal 2(1): 92106 Liu, L.M. 1989. Identification of seasonal ARIMA models using a filtering method. Communications in Statistics A18: 22792288 Liu L.M., Hudak, G.B. 1992. Forecasting and time series analysis using the SCA Statistical System: Vol. 1 Scientific Computing Associates Corp., Chicago. Liu, L.M. 1999. Forecasting and time series analysis using the SCA Statistical System: Vol. 2 Scientific Computing Associates Corp., Chicago. Makridakis S., Wheelwright S.C., McGee V.E. 1983. Forecasting: Methods and applications. Wiley, New York Pankratz, A. 1991. Forecasting with dynamic regression models, New York: John Wiley and Sons Park H.J., Fuller, W.A. 1995. Alternative estimators and unit root tests for the autoregressive process. Journal of Time Series Analysis 16: 415429 Perron P. 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica, 55: 277302 Perron P., Vogelsang T.J. 1992. Nonstationary and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics, 10: 301320. Phillips P.C.B. 1987. Time series regression with a unit root. Econometrica 55: 277301. Phillips P.C.B., Perron P. 1988. Testing for a unit root in time series regression. Biometrika 75: 335346 Phillips P.C.B. 1990. Time series regression with a unit root and infinite variance errors. Econometric Theory 6: 4462 Pindyck, R.S., Rubinfeld D.L. 1998. Econometric Models and Economic Forecasts. 4th edn. McGrawHill International Editions Reilly D.P. 1980. Experiences with an automatic BoxJenkins modeling algorithm. Tiime Series Analysis Proceedings of Houston Meeting on Time Series Analysis. Amsterdam, NorthHolland Publishing Reynolds S.B., Mellichamp J.M., Smith R.E. 1995. BoxJenkins forecast model identification. AI Expert, June, 1528 Saad E.W., Prokhorov D.V., Wunsch D.C. 1998. Comparative study of stock trend prediction using time delay, recurrent and probabilistic neural networks. IEEE Transportation Neural Networks 9(6): 14561469 Sanchez I. 2003. Efficient forecasting in nearly nonstationary processes. Journal of Forecasting, in prepapration Shin D.W., 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., 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 Tsay R.S., Tiao, G.C. 1984. Consistent estimates of autoregressive parameters and extended sample autocorrelation function for stationary and nonstationary ARMA models. Journal of American Statistical Association 79: 8496 Tsay R.S., Tiao, G.C. 1985. Use of canonical analysis in time series model identification. Biometrika 72: 299315 Xiao Z., 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., 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/31841 