Answer: 31.04

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

Author: Nikitesh Somanthe