SAS/Ets User's Guide 174. 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 | 1722 F Chapter 26 The STATESPACE Procedure Figure shows a schematic representation of the partial autocorrelations similar to the autocorrelations shown in Figure . The selection of a second order autoregressive model by the AIC statistic looks reasonable in this case because the partial autocorrelations for lags greater than 2 are not significant. Next the Yule-Walker estimates for the selected autoregressive model are printed. This output shows the coefficient matrices of the vector autoregressive model at each lag. Selected State Space Model Form and Preliminary Estimates After the autoregressive order selection process has determined the number of lags to consider the canonical correlation analysis phase selects the state vector. By default output for this process is not printed. You can use the CANCORR option to print details of the canonical correlation analysis. See the section Canonical Correlation Analysis Options on page 1731 for an explanation of this process. After the state vector is selected the state space model is estimated by approximate maximum likelihood. Information from the canonical correlation analysis and from the preliminary autoregression is used to form preliminary estimates of the state space model parameters. These preliminary estimates are used as starting values for the iterative estimation process. The form of the state vector and the preliminary estimates are printed next as shown in Figure . Figure Preliminary Estimates of State Space Model The STATESPACE Procedure Selected Statespace Form and Preliminary Estimates State Vector x T T y T T x T 1 T Estimate of Transition Matrix 0 0 1 Input Matrix for Innovation 10 01 Variance Matrix for Innovation Automatic State Space Model Selection F 1723 Figure first prints the state vector as X T T Y T T X T 1 T . This notation indicates that the state vector is zt xt
