Financial Risk Manager Part 1

Explanation:

Statement I is correct: The Q-statistic (both Box-Pierce and Ljung-Box variants) measures the degree to which autocorrelations deviate from zero and tests whether white noise is present in a dataset. It's used to test the null hypothesis that a series is white noise.

Statement II is incorrect: The Box-Pierce Q-statistic represents the sum of squared autocorrelations, not the weighted sum. The formula for Box-Pierce Q-statistic is:

$Q_{BP} = n \sum_{k=1}^{m} \hat{\rho}_k^2$

where n is the sample size, m is the number of lags, and $\hat{\rho}_k$ is the autocorrelation at lag k.

Statement III is incorrect: The Ljung-Box Q-statistic represents the weighted sum of squared autocorrelations, not the simple sum. The formula for Ljung-Box Q-statistic is:

$Q_{LB} = n(n+2) \sum_{k=1}^{m} \frac{\hat{\rho}_k^2}{n-k}$

The Ljung-Box statistic is a modified version that has better small-sample properties than the Box-Pierce statistic.

Since only Statement I is correct, the correct answer is A. Only I.