Box-Pierce Q test for autocorrelation

Formula: \(Q = n \sum_{k=1}^{m} r_k^2\), chi-square on lags - fitdf degrees of freedom. This is the uncorrected portmanteau statistic; Ljungbox applies the small-sample variance correction to the same sum.

Usage

Boxpierce(x, lags = 1, fitdf = 0)

Arguments

x

Series, normally a residual series.

lags

Number of lags entering the sum.

fitdf

Parameters fitted to obtain x.

Value

List with statistic, p_value, df, acf, n, method.

References

Box and Pierce (1970), JASA 65:1509-1526. Paywalled; the statistic was taken from R's stats::Box.test, which codes the Box-Pierce branch as n*sum(obs^2).

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Boxpierce(V)
#> $statistic
#> [1] 3.125
#> 
#> $p_value
#> [1] 0.07709987
#> 
#> $df
#> [1] 1
#> 
#> $acf
#> [1] 0.625
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Box-Pierce Q test"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"