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SAS/Ets 9.22 User's Guide 114. 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 | 1122 F Chapter 18 The MODEL Procedure Figure 18.48 Static Estimation Results for Fish Model The MODEL Procedure Nonlinear OLS Parameter Estimates Approx Approx Parameter Estimate Std Err t Value Pr t ku 0.180159 0.0312 5.78 0.0044 ke 0.524661 0.1181 4.44 0.0113 To perform a dynamic estimation of the differential equation add the DYNAMIC option to the FIT statement. proc model data fish parm ku .3 ke .3 dert.conc ku - ke conc fit conc time day dynamic run The equation DERT.CONC is integrated from conc 0 0. The results from this estimation are shown in Figure 18.49. Figure 18.49 Dynamic Estimation Results for Fish Model The MODEL Procedure Nonlinear OLS Parameter Estimates Approx Approx Parameter Estimate Std Err t Value Pr t ku 0.167109 0.0170 9.84 0.0006 ke 0.469033 0.0731 6.42 0.0030 To perform a dynamic estimation of the differential equation and estimate the initial value use the following statements proc model data fish parm ku .3 ke .3 concO 0 dert.conc ku - ke conc fit conc initial conc concO time day dynamic run The INITIAL option in the FIT statement is used to associate the initial value of a differential equation with a parameter. The results from this estimation are shown in Figure 18.50. Ordinary Differential Equations F 1123 Figure 18.50 Dynamic Estimation with Initial Value for Fish Model The MODEL Procedure Nonlinear OLS Parameter Estimates Parameter Estimate Approx Std Err t Value Approx Pr t ku 0.164408 0.0230 7.14 0.0057 ke 0.45949 0.0943 4.87 0.0165 concO 0.003798 0.0174 0.22 0.8414 Finally to estimate the fish model by using the analytical solution use the following statements proc model data fish parm ku .3 ke .3 conc ku ke 1 -exp -ke day fit conc run The results from this estimation are shown in Figure 18.51. Figure 18.51 Analytical Estimation Results for Fish Model The MODEL Procedure Nonlinear OLS Parameter Estimates Approx Approx Parameter Estimate Std Err t Value Pr t ku 0.167109 0.0170 9.84 0.0006 ke 0.469033 0.0731 6.42 0.0030 A .
