The Ljung-Box (1978) modified portmanteau test. In the
multivariate time series, this test statistic is asymptotically equal to
Hosking.
This method and the bottom documentation is taken directly from the original 'portes' package.
LjungBox(
obj,
lags = seq(5, 30, 5),
order = 0,
season = 1,
squared.residuals = FALSE
)a univariate or multivariate series with class "numeric", "matrix", "ts", or ("mts" "ts"). It can be also an object of fitted time-series model with class "ar", "arima0", "Arima", ("ARIMA forecast ARIMA Arima"), "lm", ("glm" "lm"), or "varest". obj may also an object with class "list" (see details and following examples).
vector of lag auto-cross correlation coefficients used for
Hosking test.
Default is zero for testing the randomness of a given sequence with class "numeric", "matrix", "ts", or ("mts" "ts"). In general order equals to the number of estimated parameters in the fitted model. If obj is an object with class "ar", "arima0", "Arima", "varest", ("ARIMA forecast ARIMA Arima"), or "list" then no need to enter the value of order as it will be automatically determined. For obj with other classes, the order is needed for degrees of freedom of asymptotic chi-square distribution.
seasonal periodicity for testing seasonality. Default is 1 for testing the non seasonality cases.
if TRUE then apply the test on the squared values.
This checks for Autoregressive Conditional Heteroscedastic, ARCH,
effects. When squared.residuals = FALSE, then apply the test on the usual
residuals.
The Ljung and Box test statistic with the associated p-values for different
lags based on the asymptotic chi-square distribution with k^2(lags-order)
degrees of freedom.
However the portmanteau test statistic can be applied directly on the output objects from the built in R functions ar(), ar.ols(), ar.burg(), ar.yw(), ar.mle(), arima(), arim0(), Arima(), auto.arima(), lm(), glm(), and VAR(), it works with output objects from any fitted model. In this case, users should write their own function to fit any model they want, where they may use the built in R functions FitAR(), garch(), garchFit(), fracdiff(), tar(), etc. The object obj represents the output of this function. This output must be a list with at least two outcomes: the fitted residual and the order of the fitted model (list(res = ..., order = ...)). See the following example with the function FitModel().
Note: In stats R, the function Box.test was built to compute the Box and Pierce (1970) and Ljung and Box (1978) test statistics only in the univariate case where we can not use more than one single lag value at a time. The functions BoxPierce and LjungBox are more accurate than Box.test function and can be used in the univariate or multivariate time series at vector of different lag values as well as they can be applied on an output object from a fitted model described in the description of the function BoxPierce.
Ljung, G.M. and Box, G.E.P (1978). "On a Measure of Lack of Fit in Time Series Models". Biometrika, 65, 297-303.
x <- rnorm(100)
LjungBox(x) # univariate test
#> lags statistic df p-value
#> 5 8.417892 5 0.13465910
#> 10 15.644945 10 0.11025738
#> 15 25.476588 15 0.04389770
#> 20 31.513742 20 0.04876330
#> 25 37.387808 25 0.05302203
#> 30 38.492365 30 0.13751336
x <- cbind(rnorm(100),rnorm(100))
LjungBox(x) # multivariate test
#> lags statistic df p-value
#> 5 19.16777 20 0.5109460
#> 10 40.73415 40 0.4379796
#> 15 71.13872 60 0.1538739
#> 20 93.38942 80 0.1453287
#> 25 110.90987 100 0.2142389
#> 30 136.12254 120 0.1491633