The Box-Pierce Q-statistic is calculated using the formula:
QBPβ=nβk=1mβΟk2β
Where:
- n = sample size (300)
- Οkβ = autocorrelation coefficient at lag k
- m = number of lags (3)
Plugging in the values:
QBPβ=300Γ(0.252+(β0.1)2+(β0.05)2)
QBPβ=300Γ(0.0625+0.01+0.0025)
QBPβ=300Γ0.075
QBPβ=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.