First, determine the empirical auto-correlation $\hat{\rho}_i$ of squared residuals for a lag length of up to $m$

$$ \hat{\rho}i = \dfrac{\sum{t=i+1}^{T} (\epsilon^2_t - \bar{\epsilon}^2)(\epsilon^2{t-i} - \bar{\epsilon}^2)}{\sum_{t=1}^T (\epsilon^2_t - \bar{\epsilon}^2)^2},\quad 0 \leq i < T-1 $$

where $\bar{\epsilon}^2$ is the sample mean of $\{\epsilon^2_t\}_t$.

Second,

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Third, Test statistic:

$$ Q(m) = T(T+2) \sum_{l=1}^{m} \frac{\hat{\rho}^2_l}{T-l}. $$

Reject $H_0$ if $Q(m) > \chi^2_{100(1-\alpha)}(m)$, or $p < \alpha$