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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:
     
    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
        

    plot generated by sample program

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

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