
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.
"Introduction to Time Series and Forecasting", 2nd. Ed., Peter Brockwell and Richard Davis, Springer, 2002, p. 36.
READ NEGIZ4.DAT X1 X2 Y ARMA Y 2 1 0 LET NUMLAG = 25 LJUNGBOX TEST RESDataplot generates the following output for the LjungBox test: ************************** ** ljungbox test res ** ************************** LJUNGBOX TEST FOR RANDOMNESS 1. STATISTICS: NUMBER OF OBSERVATIONS = 559 LAG TESTED = 25 LAG 1 AUTOCORRELATION = 0.1012441E02 LAG 2 AUTOCORRELATION = 0.6160716E02 LAG 3 AUTOCORRELATION = 0.5182213E02 LJUNGBOX TEST STATISTIC = 31.93575 2. PERCENT POINTS OF THE REFERENCE CHISQUARE DISTRIBUTION (REJECT HYPOTHESIS OF RANDOMNESS IF TEST STATISTIC VALUE IS GREATER THAN PERCENT POINT VALUE) FOR LJUNGBOX TEST STATISTIC 0 % POINT = 0. 50 % POINT = 24.33659 75 % POINT = 29.33885 90 % POINT = 34.38158 95 % POINT = 37.65248 99 % POINT = 44.31411 3. CONCLUSION (AT THE 5% LEVEL): THE DATA ARE RANDOM.
Date created: 3/10/2003 