SAS/Ets User's Guide 18. 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 | 162 F Chapter 5 SAS Macros and Functions where n is the number of observations 1 is the n-dimensional column vector of 1s 2 is the variance of the white noise X X1 Xn 0 and Xxx is the covariance matrix of X. On the other hand if the log-transformed time series Yt ln Xt c is a stationary pth order autoregressive process the log-likelihood function of Xt is . . n n MO - ln 2M - ln xyy - 2 ln -2 1 n - 2-2 Y - 1 y yy1 Y - 1My - Eln Xt c where y is the mean of Yt Y Y1 Yn and Xyy is the covariance matrix of Y. The LOGTEST macro compares the maximum values of l1 and lo and determines which is larger. The LOGTEST macro also computes the Akaike Information Criterion AIC Schwarz s Bayesian Criterion SBC and residual mean squared error based on the maximum likelihood estimator for the autoregressive model. For the mean squared error retransformation of forecasts is based on Pankratz 1983 pp. 256-258 . After differencing as specified by the DIF option the process is assumed to be a stationary autoregressive process. You might want to check for stationarity of the series using the DFTEST macro. If the process is not stationary differencing with the DIF option is recommended. For a process with moving average terms a large value for the AR option might be appropriate. Functions PROBDF Function for Dickey-Fuller Tests The PROBDF function calculates significance probabilities for Dickey-Fuller tests for unit roots in time series. The PROBDF function can be used wherever SAS library functions can be used including DATA step programs SCL programs and PROC MODEL programs. Syntax PROBDF x n d type x is the test statistic. n is the sample size. The minimum value of n allowed depends on the value specified for the third argument d. For d in the set 1 2 4 6 12 n must be an integer greater than or equal to max 2d 5 for other values of d the minimum value of n is 24. PROBDF Function for Dickey-Fuller Tests F 163 d is an optional integer giving the degree of the unit root tested for. .
