AUTOCORRELATION BAND

AUTOCORRELATION BAND (SET)

Set Subcommand

Specify what type of confidence bands are drawn on subsequent autocorrelation plots.

Autocorrelation plots are used for the following two purposes:
1. 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.

2. 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.

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.

SET AUTOCORRELATION BAND WHITE NOISE
SET AUTOCORRELATION BAND BOX JENKINS

The default is WHITE NOISE.

ARMA, ARIMA, BOXJENKINS, BOX, and JENKINS are synonyms for BOX JENKINS. Any other text reverts to the default choice of WHITE NOISE.

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.

Time Series Analysis

2003/2

 
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