Answer: 22.74

**Formula:** Q(m) = n(n + 2) Σ[ρ_j² / (n - j)] In this case, time lag m = 3 Thus, Q(3) = 300(302)[ (0.25)²/299 + (-0.1)²/298 + (-0.05)²/297 ] = 22.74 **Explanation:** The Ljung-Box Q statistic is used to test whether a group of autocorrelations of a time series are different from zero. The formula is: Q(m) = n(n + 2) Σ[ρ_j² / (n - j)] from j=1 to m Where: - n = number of observations (300) - m = number of lags (3) - ρ_j = autocorrelation coefficient at lag j Calculation: 1. n(n+2) = 300 × 302 = 90,600 2. Summation term: - For lag 1: (0.25)²/299 = 0.0625/299 ≈ 0.00020903 - For lag 2: (-0.1)²/298 = 0.01/298 ≈ 0.00003356 - For lag 3: (-0.05)²/297 = 0.0025/297 ≈ 0.00000842 3. Sum = 0.00020903 + 0.00003356 + 0.00000842 ≈ 0.00025101 4. Q(3) = 90,600 × 0.00025101 ≈ 22.74 The correct answer is 22.74 (Option B).

Author: Nikitesh Somanthe