Financial Risk Manager Part 1

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The following sample autocorrelation estimates are obtained using 250 data points:

Lag	1	2	3
Coefficient	0.3	-0.15	-0.10

Compute the value of the Ljung Box Q statistic.

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NNikitesh

Last updated: February 2, 2026 at 10:22

31.04

Explanation:

The Ljung Box statistic, also known as the modified Box Pierce statistic, is a function of the accumulated autocorrelations, $\rho_i$ up to time lag $m$ . It's calculated as:

Q(m) = n(n + 2)\sum_{i=1}^{m} \left(\frac{\rho_i^2}{n - i}\right)

In this case, time lag = 3

Thus,

Q(3) = 250 \times 252\left(\frac{0.3^2}{249}\right) + 250 \times 252\left(\frac{-0.15^2}{248}\right) + 250 \times 252\left(\frac{-0.1^2}{247}\right) = 31.04

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