Financial Risk Manager Part 1

The Box-Pierce Q-statistic is calculated using the formula:

$Q_{\text{BP}} = n \sum \rho_k^2$

Where:

• $n$ is the sample size (300)
• $\rho_k$ represents the autocorrelations at each lag

Given the autocorrelation coefficients:

• Lag 1: 0.25
• Lag 2: -0.1
• Lag 3: -0.05

Calculation: $Q_{\text{BP}} = 300(0.25^2 + (-0.1)^2 + (-0.05)^2)$ $Q_{\text{BP}} = 300(0.0625 + 0.01 + 0.0025)$ $Q_{\text{BP}} = 300(0.075) = 22.5$

Note: The Box-Pierce and Ljung-Box tests typically arrive at the same result when the sample size is large.