Answer: 22.5

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.

Author: Tanishq Prabhu