
LJUNGBOX TESTName:
More formally, the LjungBox test can be defined as follows.
The LjungBox test is commonly used in ARIMA modeling. Note that it is applied to the residuals of a fitted ARIMA model, not the original series.
where <y> is the response variable being tested; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LJUNGBOX TEST Y1 SUBSET TAG > 1
LET LAG = <value> LET NUMLAG = <value> By default, Dataplot will use the same number of lags as the autocorrelation plot. Typically, you will want to test fewer lags. Although the choice is somewhat arbitrary, 25 is a reasonable number for many series.
In addition to the above LET command, builtin statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).
Peter Brockwell and Richard Davis 2002, "Introduction to Time Series and Forecasting," 2nd. Ed., Springer, p. 36.
READ NEGIZ4.DAT X1 X2 Y ARMA Y 2 1 0 LET NUMLAG = 25 SET WRITE DECIMALS 4 LJUNGBOX TEST RESDataplot generates the following output for the LjungBox test: LjungBox Test for Randomness Response Variable: RES H0: The Data Are Random Ha: The Data Are Not Random Summary Statistics: Number of Observations: 559 Lag Tested: 24 Lag 1 Autocorrelation: 0.0010 Lag 2 Autocorrelation: 0.0062 Lag 3 Autocorrelation: 0.0052 LjungBox Test Statistic: 31.9107 CDF Value: 0.8708 PValue: 0.1292 Conclusions (Upper OneTailed Test)  Null Null Confidence Test Critical Hypothesis Hypothesis Level Statistic Value (>) Conclusion  Random 0.0% 31.9107 0.0000 REJECT Random 50.0% 31.9107 23.3367 REJECT Random 75.0% 31.9107 28.2412 REJECT Random 90.0% 31.9107 33.1962 ACCEPT Random 95.0% 31.9107 36.4150 ACCEPT Random 97.5% 31.9107 39.3641 ACCEPT Random 99.0% 31.9107 42.9798 ACCEPT Random 99.9% 31.9107 51.1786 ACCEPT  
Date created: 03/10/2003 Last updated: 12/11/2023 Please email comments on this WWW page to alan.heckert@nist.gov. 