Answer: 11.7

**Explanation:** The Box-Pierce Q-statistic is calculated using the formula: $$Q_{BP} = T \sum_{\tau=1}^{m} \hat{\rho}^2(\tau)$$ Where: - T = Sample size = 200 - m = Number of lags = 4 - $\hat{\rho}(\tau)$ = Autocorrelation coefficient at lag τ **Step-by-step calculation:** 1. Square each autocorrelation coefficient: - Lag 1: (0.15)² = 0.0225 - Lag 2: (-0.14)² = 0.0196 - Lag 3: (-0.1)² = 0.01 - Lag 4: (-0.08)² = 0.0064 2. Sum the squared coefficients: 0.0225 + 0.0196 + 0.01 + 0.0064 = 0.0585 3. Multiply by sample size T: 200 × 0.0585 = 11.7 Therefore, the Box-Pierce Q-statistic is 11.7, which corresponds to option C. **Note:** The Box-Pierce Q-statistic tests whether a group of autocorrelations of a time series are different from zero. It is approximately distributed as a chi-square distribution with m degrees of freedom under the null hypothesis of no autocorrelation.

Author: Nikitesh Somanthe