TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 39

SAS/Ets User's Guide 39. 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 | 372 F Chapter 8 The AUTOREG Procedure The unconditional sum of squares for the model S is S n V 1n e0e The ULS estimates are computed by minimizing S with respect to the parameters fl and . The full log likelihood function for the autoregressive error model is 1 - N ln 2 - N W2 - 1 ln IV I - where V denotes determinant of V. For the ML method the likelihood function is maximized by minimizing an equivalent sum-of-squares function. Maximizing l with respect to a2 and concentrating a2 out of the likelihood and dropping the constant term NNln 2 1 ln N produces the concentrated log likelihood function lc - N ln S I V 11 N Rewriting the variable term within the logarithm gives Sml L 1 N e0e L 1 N PROC AUTOREG computes the ML estimates by minimizing the objective function Sml L 1 N e0e L 1 N. The maximum likelihood estimates may not exist for some data sets Anderson and Mentz 1980 . This is the case for very regular data sets such as an exact linear trend. Computational Methods Sample Autocorrelation Function The sample autocorrelation function is computed from the structural residuals or noise nt yt x b where b is the current estimate of fl. The sample autocorrelation function is the sum of all available lagged products of nt of order j divided by j where is the number of such products. If there are no missing values then j N the number of observations. In this case the Toeplitz matrix of autocorrelations R is at least positive semidefinite. If there are missing values these autocorrelation estimates of r can yield an R matrix that is not positive semidefinite. If such estimates occur a warning message is printed and the estimates are tapered by exponentially declining weights until R is positive definite. Data Transformation and the Kalman Filter The calculation of V from for the general AR m model is complicated and the size of V depends on the number of observations. Instead of actually calculating V and performing GLS in the usual way in practice a Kalman filter .

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• Hướng dẫn sử dụng SAS ETS
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