# 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\$, vif\$
```

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Hildreth-Lu Technique for Autocorrelation Correction

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Seemingly Unrelated Regressions