Explanation:
Given:
Hypothesis Testing:
Decision Rule:
Analysis:
Conclusion: Both test statistics are below the critical value of 36.41, so we fail to reject the null hypothesis that the series is white noise at 95% confidence level.
Note: The Ljung-Box test is generally preferred over Box-Pierce for small samples as it has better finite-sample properties. However, in this case, both tests lead to the same conclusion.
Correct Answer: A - With 95% confidence, you accept the series as white noise (more accurately, you fail to reject the null).
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For a certain time series, you have produced a correlogram with an autocorrelation function that includes twenty four monthly observations; . Your calculated Box-Pierce Q-statistic is 19.50 and your calculated Ljung-Box Q-statistic is 27.90. You want to determine if the series is white noise. Which is your best conclusion (given CHISQ.INV(0.95, 24) = 36.41)?
A
With 95% confidence, you accept the series as white noise (more accurately, you fail to reject the null).
B
With 95% confidence, you accept the series as partial white noise (due to Box-Pierce) but reject the null (due to Ljung-Box).
C
With 95% confidence, you reject both null hypotheses and conclude the series is not white noise.
D
With 95% confidence, you reject both null hypotheses but conclude the series is white noise.
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