SAS/Ets User's Guide 80. 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 | 782 F Chapter 14 The EXPAND Procedure TOTAL indicates that the data values represent period totals for the time interval corre- sponding to the observation. AVERAGE indicates that the data values represent period averages. DERIVATIVE requests that the output series be the derivatives of the cubic spline curve fit to the input data by the SPLINE method. If only one value is specified in the OBSERVED option that value applies to both the input and the output series. For example OBSERVED TOTAL is the same as OBSERVED TOTAL TOTAL which indicates that the input values represent totals over the time intervals corresponding to the input observations and the converted output values also represent period totals. The value DERIVATIVE can be used only as the second OBSERVED option value and it can be used only when METHOD SPLINE is specified or is the default method. Since the TOTAL AVERAGE MIDDLE and END cases require that the width of each input interval be known both the FROM option and an ID statement are normally required if one of these observation characteristics is specified for any series. However if the FROM option is not specified each input interval is assumed to extend from the ID value for the observation to the ID value of the next observation and the width of the interval for the last observation is assumed to be the same as the width for the next to last observation. Scale of OBSERVED AVERAGE Values The average values are assumed to be expressed in the time units defined by the FROM or TO option. That is the product of the average value for an interval and the width of the interval is assumed to equal the total value for the interval. For purposes of interpolation OBSERVED AVERAGE values are first converted to OBSERVED TOTAL values using this assumption and then the interpolated totals are converted back to averages by dividing by the widths of the output intervals. For example suppose the options FROM MONTH TO HOUR and OBSERVED AVERAGE are specified. Since .
