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ARMA Models and the Box–Jenkins Methodology
Author(s) -
MAKRIDAKIS SPYROS,
HIBON MICHÈLE
Publication year - 1997
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/(sici)1099-131x(199705)16:3<147::aid-for652>3.0.co;2-x
Subject(s) - box–jenkins , autoregressive integrated moving average , autoregressive–moving average model , econometrics , sample (material) , computer science , moving average , time series , series (stratigraphy) , statistics , autoregressive model , mathematics , paleontology , chemistry , chromatography , biology
The purpose of this paper is to apply the Box–Jenkins methodology to ARIMA models and determine the reasons why in empirical tests it is found that the post‐sample forecasting the accuracy of such models is generally worse than much simpler time series methods. The paper concludes that the major problem is the way of making the series stationary in its mean (i.e. the method of differencing) that has been proposed by Box and Jenkins. If alternative approaches are utilized to remove and extrapolate the trend in the data, ARMA models outperform the models selected through Box–Jenkins methodology. In addition, it is shown that using ARMA models to seasonally adjusted data slightly improves post‐sample accuracies while simplifying the use of ARMA models. It is also confirmed that transformations slightly improve post‐sample forecasting accuracy, particularly for long forecasting horizons. Finally, it is demonstrated that AR(1), AR(2) and ARMA(1,1) models can produce more accurate post‐sample forecasts than those found through the application of Box–Jenkins methodology.© 1997 John Wiley & Sons, Ltd.