Financial Risk Manager Part 1

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

$Q_{\text{BP}} = n \sum_{k=1}^{m} \rho_k^2$

Where:

• $n$ = sample size (300)
• $\rho_k$ = autocorrelation coefficient at lag k
• $m$ = number of lags (3)

Plugging in the values:

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

Therefore, the correct answer is 22.5.

Note: The Box-Pierce Q-statistic tests whether a group of autocorrelations of a time series are different from zero. For large sample sizes, the Box-Pierce and Ljung-Box tests typically yield similar results, though the Ljung-Box test has better small-sample properties.