Multi-Seasonal Portmanteau Tests

Multi-seasonal generalisation of the Ljung-Box and Monti portmanteau tests: residual autocorrelation is checked at low-order and seasonal lags at once, for an arbitrary number of seasonal periods.

Usage

msportmanteau(
  x,
  type = c("Ljung-Box", "Monti"),
  season = NULL,
  nlag = 5,
  lags_short = 0,
  npar = NULL
)

Arguments

x: A numeric vector, a ts/msts object, or a fitted msarima model (in which case the model residuals are used).
type: Either "Ljung-Box" (default), which builds the statistic from the autocorrelations, or "Monti", which uses the partial autocorrelations. Partial matching is allowed.
season: Numeric vector of seasonal periods to test, of any length. If NULL (default) the periods are taken from the msts/ts attributes of x, or from the fitted model.
nlag: Numeric vector giving the number of seasonal multiples of each period to test, i.e. lags season * (1:nlag). A single value is recycled across season; otherwise give one value per period, e.g. c(5, 3). Default 5.
lags_short: Number of low-order, non-seasonal lags 1:lags_short added to the seasonal ones. Default 0 (none).
npar: Number of estimated model parameters. Default 0 for a raw series; for a fitted msarima model it defaults to the number of estimated (non-fixed) AR, seasonal AR, MA and seasonal MA coefficients.

Value

An object of class "htest", with:

statistic: the test statistic ("X-squared").
parameter: the degrees of freedom ("df"), the number of lags tested minus npar.
p.value: the p-value, from the upper tail of a chi-squared distribution with parameter degrees of freedom.
method: a character string describing the test.
data.name: a character string naming the data.
lag: the lags actually tested.

Details

The lag set tested is sort(unique(c(1:lags_short, outer(season, 1:nlag)))), the same construction as in the original two-season versions of these tests, generalised to any number of periods.

As in sacf, leading and trailing NAs (such as those produced by differencing in msarima) are dropped (stats::na.contiguous) before computing the statistic, and the number of observations used is the length of the series that remains.

References

Grigoletto, M. and Lisi, F. (2026). Portmanteau goodness-of-fit tests in the presence of simple, mixed, and multiple seasonal autocorrelation. arXiv. doi:10.48550/arXiv.2609.32381

Ljung, G. M. and Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297-303.

Monti, A. C. (1994). A proposal for a residual autocorrelation test in linear models. Biometrika, 81(4), 776-780.

Examples

fit <- msarima(MAD_m40, order = c(1, 0, 2),
               seasonal = list(c(0, 1, 1), c(0, 1, 1)))

# periods 24 and 168 taken from the msts object
msportmanteau(MAD_m40, nlag = 3)
#> 
#> 	Multi-seasonal Ljung-Box test
#> 
#> data:  MAD_m40
#> X-squared = 4767.5, df = 6, p-value < 2.2e-16
#> 
# residual test, periods and npar from the model
msportmanteau(fit, type = "Monti", nlag = 3)
#> 
#> 	Multi-seasonal Monti test
#> 
#> data:  MAD_m40
#> X-squared = 3.8858, df = 1, p-value = 0.0487
#>