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 The ARIMA Procedure

# Overview

The ARIMA procedure analyzes and forecasts equally spaced univariate time series data, transfer function data, and intervention data using the AutoRegressive Integrated Moving-Average (ARIMA) or autoregressive moving-average (ARMA) model. An ARIMA model predicts a value in a response time series as a linear combination of its own past values, past errors (also called shocks or innovations), and current and past values of other time series.

The ARIMA approach was first popularized by Box and Jenkins, and ARIMA models are often referred to as Box-Jenkins models. The general transfer function model employed by the ARIMA procedure was discussed by Box and Tiao (1975). When an ARIMA model includes other time series as input variables, the model is sometimes referred to as an ARIMAX model. Pankratz (1991) refers to the ARIMAX model as dynamic regression. The ARIMA procedure provides a comprehensive set of tools for univariate time series model identification, parameter estimation, and forecasting, and it offers great flexibility in the kinds of ARIMA or ARIMAX models that can be analyzed. The ARIMA procedure supports seasonal, subset, and factored ARIMA models; intervention or interrupted time series models; multiple regression analysis with ARMA errors; and rational transfer function models of any complexity.

The design of PROC ARIMA closely follows the Box-Jenkins strategy for time series modeling with features for the identification, estimation and diagnostic checking, and forecasting steps of the Box-Jenkins method.

Before using PROC ARIMA, you should be familiar with Box-Jenkins methods, and you should exercise care and judgment when using the ARIMA procedure. The ARIMA class of time series models is complex and powerful, and some degree of expertise is needed to use them correctly.

If you are unfamiliar with the principles of ARIMA modeling, refer to textbooks on time series analysis. Also refer to SAS/ETS Software: Applications Guide 1, Version 6, First Edition. You might consider attending the SAS Training Course "Forecasting Techniques Using SAS/ETS Software." This course provides in-depth training on ARIMA modeling using PROC ARIMA, as well as training on the use of other forecasting tools available in SAS/ETS software.

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