Ljung-Box test for autocorrelation (white-noise / portmanteau test)

Applies the Ljung-Box portmanteau test (Ljung & Box, 1978) to a one-dimensional signal: the statistic \(Q = N(N+2)\sum_{k=1}^{h} \hat\rho_k^2 / (N-k)\) aggregates the first lag squared autocorrelations (from autocorrelation), and under the null hypothesis that the series is white noise \(Q\) follows a chi-squared distribution with lag degrees of freedom. It is the standard formal test for the presence of autocorrelation (and, applied to model residuals, for model adequacy). Same definition as statsmodels.stats.diagnostic.acorr_ljungbox and stats::Box.test(type = "Ljung-Box").

Usage

ljungBoxTest(x, lag = 10L)

Arguments

x

A numeric vector (the time series).

lag

Number of lags \(h\) to include (default 10), and the degrees of freedom of the reference chi-squared.

Value

A list with statistic (the Ljung-Box \(Q\)), p_value (the chi-squared upper-tail probability), and df (= lag).

References

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

See also

autocorrelation, Box.test

Examples

set.seed(1)
ljungBoxTest(rnorm(500), lag = 10)$p_value   # white noise -> large p
#> [1] 0.3980809