SAS/Ets User's Guide 82. 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 | 802 F Chapter 14 The EXPAND Procedure OBSERVED a character variable containing the first letter of the OBSERVED option name for the input series the ID variable that contains the lower breakpoint or knot of the spline segment to which the coefficients apply. The ID variable has the same name as the variable used in the ID statement. If an ID statement is not used but the FROM option is used then the name of the ID variable is DATE or DATETIME depending on whether the FROM option indicates SAS date or SAS datetime values. If neither an ID statement nor the FROM option is used the ID variable is named TIME. CONSTANT the constant coefficient for the spline segment LINEAR the linear coefficient for the spline segment QUAD the quadratic coefficient for the spline segment CUBIC the cubic coefficient for the spline segment For each BY group the OUTEST data set contains observations for each polynomial segment of the spline curve fit to each input series. To obtain the observations defining the spline curve used for a series select the observations where the value of VARNAME equals the name of the series. The observations for a series in the OUTEST data set encode the spline function fit to the series as follows. Let a - bi ci and di be the values of the variables CUBIC QUAD LINEAR and CONSTANT respectively for the i th observation for the series. Let x be the value of the ID variable for the i th observation for the series. Let n be the number of observations in the OUTEST data set for the series. The value of the spline function evaluated at a point x is f x a x - Xi 3 bi x - Xi 2 Ci x - x di where the segment number i is selected as follows i xi x xi i 1 i n 1 x x1 n x xn In other words if x is between the first and last ID values x1 x xn use the observation from the OUTEST data set with the largest ID value less than or equal to x. If x is less than the first ID value x1 then i 1. If x is greater than or equal to the last ID value x xn then i n. For METHOD JOIN the .
