AUTOCORRELATION BAND
Name:
AUTOCORRELATION BAND (SET)
Type:
Purpose:
Specify what type of confidence bands are drawn on
subsequent autocorrelation plots.
Description:
Autocorrelation plots are used for the following two
purposes:
 To assess the independence (i.e., randomness) of a
set of observations.
In this case, the desired confidence bands are
\( \pm \frac{z_{1\alpha/2}} {\sqrt{N}} \)
where α is the desired significance level,
z is the percent point function of the standard normal
distribution, and N is the sample size. In this case,
the confidence bands have a fixed width.
 In the context of ARIMA models, confidence bands are
generated under the assumption that the data are from a
moving average process. In this context, confidence
bands help identify the appropriate order for the
moving average model. The formula for the confidence
bands is
\(
\pm z_{1\alpha/2} \sqrt{\frac{1}{N} (1 + 2 \sum_{i=1}^{k}{y_{i}^2})}
\)
where α is the desired significance level,
z is the percent point function of the standard normal
distribution, N is the sample size, and k is the
desired lag. In this case, the width of the confidence bands
increases as the lag, k, increases.
Syntax:
SET AUTOCORRELATION BAND <WHITE NOISE/BOX JENKINS>
where <WHITE NOISE> specifies that the confidence bands are
drawn to show independence while <BOX JENKINS> specifies
that confidence bands are drawn to identify the
order of the movign average process.
Examples:
SET AUTOCORRELATION BAND WHITE NOISE
SET AUTOCORRELATION BAND BOX JENKINS
Default:
The default is WHITE NOISE.
Synonyms:
ARMA, ARIMA, BOXJENKINS, BOX, and JENKINS are synonyms
for BOX JENKINS. Any other text reverts to the default
choice of WHITE NOISE.
Related Commands:
CORRELATION PLOT

= Generate an autocorrelation, partial autocorrelation,
or cross correlation plot.

AUTOCORRELATION LAG

= Specifies whether the lag 0 value is plotted on
subsequent autocorrelation or partial autocorrelation plots.

SPECTRAL PLOT

= Generate a spectral plot.

Applications:
Implementation Date:
Program:
READ NEGIZ4.DAT X1 X2 Y
SET AUTOCORRELATION BAND BOX JENKINS
SET AUTOCORRELATION LAG ZERO OFF
LINE BLANK
SPIKE ON
LINE COLOR BLACK BLACK BLUE BLUE RED RED
X1LABEL LAG
Y1LABEL AUTOCORRELATION
XTIC OFFSET 2 0
AUTOCORRELATION PLOT Y
