Answer: 22.5

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.

Author: Nikitesh Somanthe