Box-Ljung autocorrelation test

Ljung-Box test for autocorrelation

Usage

AutocorTest(x, lag = ceiling(log(length(x))),
            type = c("Ljung-Box", "Box-Pierce", "rank"),
            df = lag )

Arguments

x

a numeric vector or a univariate time series

lag

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.'

type

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'.

df

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.

Details

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.

Value

a list of class 'htest' containing the following components:

statistic: a number giving the value of the test statistic.
paramter: a number giving the degrees of freedom of the approximate chi-squared distribution of the test statistic used to compute the p.value.
p.value: the p-value of the test.
method: a character string indicating which type of test was performed. If(df != lag), this character string ends with paste("(lag = ", lag, ")", sep="").

Source

https://faculty.chicagobooth.edu/ruey-s-tsay/teaching

References

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.

Examples

data(m.ibm2697)
AutocorTest(m.ibm2697, 5)
#> 
#> 	Box-Ljung test
#> 
#> data:  m.ibm2697
#> X-squared = 5.4474, df = 5, p-value = 0.3638
#> 

AT4 <- AutocorTest(m.ibm2697, 5, df=4)
str(AT4) # $method = "Box-Ljung test (lag = 5)"
#> List of 6
#>  $ statistic   : Named num 5.45
#>   ..- attr(*, "names")= chr "X-squared"
#>  $ parameter   : Named num 4
#>   ..- attr(*, "names")= chr "df"
#>  $ p.value     : Named num 0.244
#>   ..- attr(*, "names")= chr "X-squared"
#>  $ method      : chr "Box-Ljung test (lag = 5)"
#>  $ data.name   : chr "m.ibm2697"
#>  $ Total.observ: int 864
#>  - attr(*, "class")= chr "htest"