New optimized model identification in time series model and its difficulties

Subject Areas : Stochastics Problems

احمدرضا  زنبوری ¹ (گروه آمار، واحد مرودشت، دانشگاه آزاد اسلامی، مرودشت، ایران)
کریم  زارع ² (گروه آمار، واحد مرودشت، دانشگاه آزاد اسلامی، مرودشت، ایران)

Received: 2017-03-14 Accepted : 2017-05-12 Published : 2017-06-01

Keywords: Time series, Outliers, Box-Jenkins, Extended sample autocorrelation function,

Abstract :

Model identification is an important and complicated step within the autoregressive integrated moving average (ARIMA) methodology framework. This step is especially difficult for integrated series. In this article first investigate Box-Jenkins methodology and its faults in detecting model, and hence have discussed the problem of outliers in time series. By using this optimization method, we will overcome this problem. The method that used in this paper is better than the Box-Jenkins in term of optimality time.

References:

Algina, J., & Swaminathan, H. A. (1977). A procedure for the analysis of time series designs. Journal of Experimental Education, 45, 56-60.

Ayat, L., & Burridge, P. (2000). Unit root tests in the presence of uncertainty about the non-stochastic trend. Journal of Econometrics, 95, 71-96.

Barnett, V. – Lewis, T. (1994) Outliers in Statistical Data. Third Edition, John Wiley & Sons, New York.

Box, G.E.P. – Jenkins, G.M. (1970, 1976) Time Series Analysis, Forecasting and Control. Revised Edition 1976, Holden-Day, San Francisco.

Box, G.E.P. (1953) Non-normality and tests on variances. Biometrika 40, 318–335.

Brockwell, P.J. – Davis, R.A. (1991) Time Series: Theory and Methods. Second Edition, Springer-Verlag, New York.

Burn, D.A. – Ord, J.K. (1984) The effect of time series outliers on the sample autocorrelation coefficient. American Statistical Association, Proceedings of the Business and Economic Statistics Section, 581–585.

Chan, Wai-Sum (1992) A note on time series model specification in the presence of outliers. Journal of Applied Statistics 19, 117–124.

Chan, Wai-Sum (1995) Understanding the effect of time series outliers on sample autocorrelations. Test 4, 179–186.

Chang, I. – Tiao, G.C. – Chen, C. (1988) Estimation of time series parameters in the presence of outliers. Technometrics 30 193–204.

Choi, B. S. (1992). ARMA model identification. New York: Springer.

De Gooijer, J.G. – Abraham, B. – Gould, A. – Robinson, L. (1985) Methods for determining the order of an autoregressive moving average process: a survey. International Statistical Review 53, 301–329.

Denby, R. – Martin, R.D. (1979) Robust estimation of the first order autoregressive parameter. Journal of the American Statistical Association 74, 140–146

Durbin, J. (1979) ‘Discussion’ of Kleiner, B., Martin, R.D. and Thomson, D.J. (1979),  Robust estimation of power spectra.  338–339, Journal of the Royal Statistical Society B 41.

Elder, J., & Kennedy, P. E. (2001b). Testing for unit roots: What should students be taught? Journal of Economic Education, 32, 137-146.

Fox, A.J. (1972) Outliers in time series. Journal of the Royal Statistical Society B 34, 350–363.

Franke, J. – Hardle, W. – Martin, D. (eds.) (1984) Robust and Nonlinear Time Series Analysis. Springer-Verlag, New York.

Fuller, W.A. (1996) Introduction to Statistical Time Series. Second Edition, Wiley, New York.

Funke, M. (1992) Time-series forecasting of the German unemployment rate. Journal of Forecasting 11, 111–125.

Gather, U. – Becker, C. (1997) Outlier identification and robust methods. In: Handbook of Statistics 15: Robust Inference (eds. G.S. Maddala and C.R. Rao), 123–143, Elsevier, Amsterdam.

Glass, G. V., Willson, V. L., & Gottman, J. M. (1975). Design and analysis of time-series experiments. Boulder, CO: Colorado Associated University Press.

Huber, P.J. (1964) Robust estimation of a location parameter. Annals of Mathematical Statistics 35, 73–101.

Huber, P.J. (1973) Robust regression: Asymptotic, conjectures and Monte Carlo. The Annals of Statistics 1, 799–821.

Kelly, G. (1992) Robust regression estimators. The choice of tuning constants. The Statistician 41, 303–314.

Kendall, M. G., & Buckland, W. R. (1971). A dictionary of statistic terms. New York: Hafner Publishing Company.

Kleiner, B. – Martin, R.D. – Thomson, D.J. (1979) Robust estimation of power spectra (with discussion). Journal of the Royal Statistical Society, B 41, 313–351.

Koreisha, S.G. – Yoshimoto, G. (1991) A comparison among identification procedures for autoregressive moving average models. International Statistical Review 59, 37–57.

Künsch, H.R. (1984) Infinitesimal robustness for autoregressive processes. The Annals of Statistics 12, 843–863.

Li, S. – Dickinson, B.W. (1988) Application of the Lattice Filter to Robust Estimation of AR and ARMA Models. IEEE, Trans. Acoustics, Speech, and Signal Processing, Vol. 36, 502–512.

Martin, R.D. (1981) Robust methods for time series. In: Applied Time Series Analysis II, ed. by D.F. Findley, 683–759, Academic Press, New York.

Mohammadi, K., Eslami, H.R., Kahawita, R., 2006. Estimation of an ARMA model for river flow forecasting using goal programming. Journal of Hydrology 331 (1–2), 293–299.

Quinn, B.G. (1980) Limiting behavior of autocorrelation function of ARMA process as several roots of characteristic equation approach unit circle. Communications in Statistics – Simulation and Computation, B9(2), 195–198.

Stadnytska, T., Braun, S., & Werner, J. (2008). Comparison of automated procedures for ARMA model identification. Behavior Research Methods. 40(1), 250-262

Stadnytska, T., Braun, S., & Werner, J. (2008). Model identification of integrated ARMA processes. Multivariate Behavioral Research, 43:1–28.

Tiao, G.C. – Tsay, R.S. (1981) Identification of nonstationary and stationary ARMA models. ASA Proceedings of Business and Economic Statistics Section, 308–312.

Tiao, G.C. – Tsay, R.S. (1983a) Consistent properties of least squares estimates of autoregressive parameters in ARMA models. Annals of Statistics 11, 856–871. ‘TT83’

Tiao, G.C. – Tsay, R.S. (1983b) Multiple time series modeling and extended sample cross-correlations. Journal of Business & Economic Statistics 1, 43–56.

Tiao, G.C. (1985) Autoregressive moving average models, intervention problems and outlier detection in time series. In: Handbook of Statistics, Vol. 5, E.J. Hannan, P.R. Krishnaiah and M.M. Rao, eds, 85–118.

Tiao, G.C. (2001) Univariate autoregressive moving-average models. In: A Course in Time Series Analysis, G.C. Tiao and R.S. Tsay; 53–85, John Wiley & Sons, New York.

Tsay, R.S. (1984) Regression models with time series errors. Journal of the American Statistical Association, 79, 118–124.

Tsay, R.S. (1986) Time series model specification in the presence of outliers. Journal of the American Statistical Association 81, 132–141.

Velicer, W. F. & Harrop, J. W. (1983). The reliability and accuracy of time series model identification. Evaluation Review, 7, 551-560.

Velicer, W. F., & McDonald, R. P. (1984). Time series analysis without model identification. Multivariate Behavioral Research, 19, 33-47.

Wang, W. – Wei, W.W.S. (1993) Robust estimation of autocorrelation function. ASA Proceedings of Business and Economic Statistics Section, 175–180.

Wei, W.W.S. (1990, 1994) Time Series Analysis, Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Inc. Redwood City, California, Reprinted with corrections, February 1994.

Zanboori E., Hosseinzadeh  Lotfi F., Rostamy-Malkhalifeh M. and Jahanshahloo G., (2014) Computing Relative weights in AHP and Ranked Units in the Presence of Large Dimensionality of data set based on Orthogonal Gram Schmidt Technique. Adv. Environ. Biol., 8 (21), 78-81.