Ljung-Box test for autocorrelation
AutocorTest(x, lag = ceiling(log(length(x))),
type = c("Ljung-Box", "Box-Pierce", "rank"),
df = lag )
a list of class 'htest' containing the following components:
a number giving the value of the test statistic.
a number giving the degrees of freedom of the approximate chi-squared distribution of the test statistic used to compute the p.value.
the p-value of the test.
a character string indicating which type of test was performed. If(df != lag), this character string ends with paste("(lag = ", lag, ")", sep="").
a numeric vector or a univariate time series
the statistic will be based on 'lag' autocorrelation coefficients. Tsay (p. 27-28) says, 'Simulation studies suggest that the choice of [lag = log(length(x))] provides better power performance. This general rule needs modification in analysis of seasonal time series for which autocorrelations with lags at multiples of the seasonality are more important.'
which Box.test 'type' should be used? Partial matching is used.
The 'rank' alternative computes 'Ljung-Box' on rank(x); see Burns (2002) and references therein.
NOTE: The default 'Ljung-Box' type generally seems to be more accurate and popular than the earlier 'Box-Pierce', which is however the default for 'Box.test'.
a positive number giving the degrees of freedom for the reference chi-squre distribution used to compute the p-value for the statistic.
This makes it easy to call AutocorTest with the residuals from a fit
and have the p-value computed with reference to a chi-square with
degrees of freedom different from "lag". See the discussion
of degrees of freedom for 'Box.test in ARIMA
.
This is provided for compatibility with 'autocorTest' in the S-Plus
script in Tsay (p. 30). It is a wrapper for the R function
Box.test
.
Ruey Tsay (2005) Analysis of Financial Time Series, 2nd ed. (Wiley)
Patrick Burns (2002) 'Robustness of the Ljung-Box Test and its Rank Equivalent', https://www.burns-stat.com/pages/Working/ljungbox.pdf, accessed 2007.12.29.
Box.test
ARIMA
data(m.ibm2697)
AutocorTest(m.ibm2697, 5)
AT4 <- AutocorTest(m.ibm2697, 5, df=4)
str(AT4) # $method = "Box-Ljung test (lag = 5)"
Run the code above in your browser using DataLab