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SAS/Ets 9.22 User's Guide 23. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 212 F Chapter 7 The ARIMA Procedure Xi t ki is the ith input time series or a difference of the ith input series at time t is the pure time delay for the effect of the ith input series i B 8i B is the numerator polynomial of the transfer function for the ith input series is the denominator polynomial of the transfer function for the ith input series. The model can also be written more compactly as W P C X i .B Xit C nt where i i B is the transfer function for the ith input series modeled as a ratio of the and 8 polynomials ty B a B 8i B Bki nt is the noise series nt 0 B 0 B at This model expresses the response series as a combination of past values of the random shocks and past values of other input series. The response series is also called the dependent series or output series. An input time series is also referred to as an independent series or a predictor series. Response variable dependent variable independent variable or predictor variable are other terms often used. Notation for Factored Models ARIMA models are sometimes expressed in a factored form. This means that the 0 0 a or 8 polynomials are expressed as products of simpler polynomials. For example you could express the pure ARIMA model as Wt _ C 0i B 02 B B i B 2 B a t where 01 B 02 B 0 B and 01 B 02 B 0 B . When an ARIMA model is expressed in factored form the order of the model is usually expressed by using a factored notation also. The order of an ARIMA model expressed as the product of two factors is denoted as ARIMA p d q x P D Q . Notation for Seasonal Models ARIMA models for time series with regular seasonal fluctuations often use differencing operators and autoregressive and moving-average parameters at lags that are multiples of the length of the seasonal cycle. When all the terms in an ARIMA model factor refer to lags that are a multiple of a constant s the constant is factored out and suffixed to the ARIMA p d q notation. Thus the general notation for the order of a seasonal ARIMA model with
