tailieunhanh - SAS/ETS 9.22 User's Guide 292

SAS/Ets User's Guide 292. 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 | 2902 F Chapter 46 Forecasting Process Details The ARIMA model equivalency to double exponential smoothing is the ARIMA 0 2 2 model 1 - B 2Yt 1 - OBfet 0 1 - a The moving-average form of the equation is Yt et C f 2a C i - 1 a2 e - j 1 For double exponential smoothing the additive-invertible region is 0 a 2g The variance of the prediction errors is estimated as var et k var et k 1 1 C X 2a C j - 1 a2 2 1 1 Linear Holt Exponential Smoothing The model equation for linear exponential smoothing is Yt Ft C Pt t C et The smoothing equations are Lt aYt C 1 _ a Lt-i C Tt-i Tt y Lt - Lt-i C 1 - y Tt-i The error-correction form of the smoothing equations is Lt Lt-1 C Tt-1 C aet Tt Tt-1 C ayet Note For missing values et 0. The -step prediction equation is Yt k Lt C kTt The ARIMA model equivalency to linear exponential smoothing is the ARIMA 0 2 2 model 1 - B 2Yt 1 - 01B - 02B2 et 01 2 a ay O2 a - 1 Equations for the Smoothing Models F 2903 The moving-average form of the equation is 1 Yt et X -j j i For linear exponential smoothing the additive-invertible region is 0 a 2g 0 y 4 a - 2g The variance of the prediction errors is estimated as k var et k 1 1 X a jay 2 j 1 Damped-Trend Linear Exponential Smoothing The model equation for damped-trend linear exponential smoothing is Yt Bt Pt t Q The smoothing equations are Lt aYt 1 - a Lt-i 0T-1 Tt y Lt - Lt-i 1 - y 0T-i The error-correction form of the smoothing equations is Lt Lt-1 0Tt-1 aet Tt 0Tt-1 ayet Note For missing values et 0. The k-step prediction equation is k Yt k Lt X 0 i Tt i 1 The ARIMA model equivalency to damped-trend linear exponential smoothing is the ARIMA 1 1 2 model 1 - 0B 1 - B Yt 1 - 01B - 02 2 et 01 1 0 a ay0 02 a - 1 0 2904 F Chapter 46 Forecasting Process Details The moving-average form of the equation assuming 0 1 is Yt X 0 0j - 1 0 - 1 er-j j 1 For damped-trend linear exponential smoothing the additive-invertible region is 0 2g 0 0 4 2g The variance of the prediction errors is estimated as var et k .