tailieunhanh - SAS/ETS 9.22 User's Guide 27

SAS/Ets User's Guide 27. 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 | 252 F Chapter 7 The ARIMA Procedure Estimation Details The ARIMA procedure primarily uses the computational methods outlined by Box and Jenkins. Marquardt s method is used for the nonlinear least squares iterations. Numerical approximations of the derivatives of the sum-of-squares function are taken by using a fixed delta controlled by the DELTA option . The methods do not always converge successfully for a given set of data particularly if the starting values for the parameters are not close to the least squares estimates. Back-Forecasting The unconditional sum of squares is computed exactly thus back-forecasting is not performed. Early versions of SAS ETS software used the back-forecasting approximation and allowed a positive value of the BACKLIM option to control the extent of the back-forecasting. In the current version requesting a positive number of back-forecasting steps with the BACKLIM option has no effect. Preliminary Estimation If an autoregressive or moving-average operator is specified with no missing lags preliminary estimates of the parameters are computed by using the autocorrelations computed in the IDENTIFY stage. Otherwise the preliminary estimates are arbitrarily set to values that produce stable polynomials. When preliminary estimation is not performed by PROC ARIMA then initial values of the coefficients for any given autoregressive or moving-average factor are set to if the degree of the polynomial associated with the factor is 9 or less. Otherwise the coefficients are determined by expanding the polynomial 1 to an appropriate power by using a recursive algorithm. These preliminary estimates are the starting values in an iterative algorithm to compute estimates of the parameters. Estimation Methods Maximum Likelihood The METHOD ML option produces maximum likelihood estimates. The likelihood function is maximized via nonlinear least squares using Marquardt s method. Maximum likelihood estimates are more expensive to compute than the .