Answer-first summary for fast verification
Answer: With 95% confidence, you accept the series as white noise (more accurately, you fail to reject the null).
## Explanation **Given:** - Sample size: 24 observations (m = degrees of freedom = 24) - Box-Pierce Q-statistic = 19.50 - Ljung-Box Q-statistic = 27.90 - Critical value: CHISQ.INV(0.95, 24) = 36.41 **Hypothesis Testing:** - H₀: All autocorrelations are zero (series is white noise) - H₁: At least some autocorrelations are non-zero (series is not white noise) **Decision Rule:** - If test statistic < critical value → Fail to reject H₀ (accept white noise) - If test statistic > critical value → Reject H₀ (reject white noise) **Analysis:** - Box-Pierce Q = 19.50 < 36.41 → Fail to reject H₀ - Ljung-Box Q = 27.90 < 36.41 → Fail to reject H₀ **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).
Author: LeetQuiz Editorial Team
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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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