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Forecast Functions Implied by Autoregressive Integrated Moving Average Models and Other Related Forecast Procedures

Bovas Abraham and Johannes Ledolter
International Statistical Review / Revue Internationale de Statistique
Vol. 54, No. 1 (Apr., 1986), pp. 51-66
DOI: 10.2307/1403258
Stable URL: http://www.jstor.org/stable/1403258
Page Count: 16
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Forecast Functions Implied by Autoregressive Integrated Moving Average Models and Other Related Forecast Procedures
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Abstract

The simplifying operators in ARIMA (autogressive integrated moving average) models determine the form of the corresponding forecast functions. For example, regular differences imply polynomial trends and seasonal differences certain periodic functions. The same functions also arise in the context of many other forecast procedures, such as regressions on time, exponential smoothing and Kalman filtering. In this paper we describe how the various methods update the coefficients in these forecast functions and discuss their similarities and differences. In addition, we compare the forecasts from seasonal ARIMA models and the forecasts from Winters' additive and multiplicative smoothing methods. /// L'application d'opérateurs simplifiant les modèles ARIMA détermine du même coup le genre de fonctions de prédiction qui en résulte. Par exemple, l'utilisation de différences finies basées sur des intervalles réguliers génère des fonctions polynomiales, tandis que les différences finies éliminant les comportements saisonniers génèrent des fonctions à caractère périodique. Ces mêmes fonctions se retrouvent dans d'autres méthodes de prédiction, telles que les régressions sur le temps, la graduation exponentielle et le filtre de Kalman. Cet article présente donc une description de l'influence des différentes méthodes sur le processus de révision des coefficients des fonctions de prédiction. Une analyse comparative de ces méthodes est aussi inclue. De plus, nous comparons les prédictions d'un modèle ARIMA saisonnier et celles des modèles (additifs et multiplicatifs) de graduation de Winters.

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