Dataplot Vol 1 Vol 2

# AUTOCORRELATION BAND

Name:
AUTOCORRELATION BAND (SET)
Type:
Set Subcommand
Purpose:
Specify what type of confidence bands are drawn on subsequent autocorrelation plots.
Description:
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.

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:
Time Series Analysis
Implementation Date:
2003/2
Program:

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


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Date created: 03/07/2003
Last updated: 10/09/2015