.. index::
   single: ARIMA
   single: Box-Jenkins
   single: Moving Averages
   single: G7 Command; ac
   single: Autocorrelation Function

ARIMA Techniques
================

**ac <series> [n]**
   Calculate the autocorrelation function for the named series over the period specified by the latest *limits* command.  The optional 'n' is the maximum number of terms to be calculated; its default value is 20.  The output shows the autocorrelation function and the autoregression coefficients determined by the Yule-Walker equations.  Taking the rightmost elements of each line of the autoregression coefficients gives the partial autocorrelation function.  The function also is placed into the workspace with a name derived by adding "_ac" to the variable's name.  This variable then can be used to graph the function.  If the command was "ac vi 20", then the graphing command would be "gr vi_ac :0 20".

   Example::

      ac vin$ 11


**bj <q> <y> = <x1>, [x2,] ..., [xn]**
   Perform a Box-Jenkins estimation for autoregressive moving average models.  Here <q> is the number of lags in the moving average error terms; e.g., with q = 2, u[t] = e[t] + b1×e[t-1] + b2×e[t-2].  This <q> must be no more than 4.  The program only will check for the stability of the solution if q <= 2.  No more than 10 independent variables, please.  At each iteration of the "Newtonian" non-linear regression algorithm, you will be allowed to intervene to try new values for the theta's, the coefficients for the moving average of error terms.  If *save* is on, the first and the final equation will be in the .SAV file with the theta  values appearing as coeffients of "theta".  These must be removed before building a model with *Build*.

   Example::

      bj 2 vif$ = vif$[1], vif$[2]