Overview
The Ljung Box test formalizes the inuition of examing the Autocorrelation of a time series into a test statistic that can be formulated as a Hypothesis Test
Test Statistic
The test statistic used in the test is
{% Q = N(N+2) \sum_{i=1}^k (N-k)^{-1} r_i^2 %}
where {% r_k %} is the autocorrelation of degree {% k %},
(that is between {% r_t %} and {% r_{t-k} %}) and {% N %} is the number of points in the time series.
This test statistic has been shown to be distributed as a
chi-square
variable with {% k %} degrees of freedom.
(see sanchez pg 128)