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.