tailieunhanh - SAS/ETS 9.22 User's Guide 200

SAS/Ets User's Guide 200. 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 | 1982 F Chapter 31 The UCM Procedure When this expression of a2 is substituted back into the likelihood formula an expression called the profile likelihood Lprofiie of the data is obtained In n 2 2Lprofile .yi --- yn Wt log Ft n d log p t 1 t I 1 t I 1 t In some situations the parameter estimation is done by optimizing the profile likelihood see the section Parameter Estimation by Profile Likelihood Optimization on page 1990 and the PROFILE option in the ESTIMATE statement . In the remainder of this section the state space formulation of UCMs is further explained by using some particular UCMs as examples. The examples show that the state space formulation of the UCMs depends on the components in the model in a simple fashion for example the system matrix T is usually a block diagonal matrix with blocks that correspond to the components in the model. The only exception to this pattern is the UCMs that consist of the lags of dependent variable. This case is considered at the end of the section. In what follows Diag a b . denotes a diagonal matrix with diagonal entries a b . and the transpose of a matrix T is denoted as T 0 . Locally Linear Trend Model Recall that the dynamics of the locally linear trend model are yt Pt Q Pt Pt-i pt-i ht Pt Pt-i tt Here yt is the response series and et ht and t are independent zero-mean Gaussian disturbance sequences with variances a2 a2 and a2 respectively. This model can be formulated as a state space model where the state vector at et pt pt and the state noise fy et ht t Note that the elements of the state vector are precisely the unobserved components in the model. The system matrices T and Z and the noise covariance Q corresponding to this choice of state and state noise vectors can be seen to be time invariant and are given by 000 Z 110 T 011 00 1 and Q Diageo2 a2 af The distribution of the initial state vector a is diffuse with P Diag a 0 0 and P1 Diag 0 1 1 . The parameter vector 9 consists of all the disturbance variances that

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