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 To determine if the time series is white noise, we compare the calculated Q-statistics with the critical chi-square value at 95% confidence level with 24 degrees of freedom, which is given as 36.41. ### Statistical Test Results: - **Box-Pierce Q-statistic** = 19.50 - **Ljung-Box Q-statistic** = 27.90 - **Critical value (χ²₀.₉₅, ₂₄)** = 36.41 ### Decision Rule: - **Null Hypothesis (H₀)**: The series is white noise (no autocorrelation) - **Rejection Rule**: If Q-statistic > critical value, reject H₀ ### Analysis: 1. **Box-Pierce (19.50)**: 19.50 < 36.41 → **Fail to reject H₀** 2. **Ljung-Box (27.90)**: 27.90 < 36.41 → **Fail to reject H₀** Both test statistics are **less than** the critical value of 36.41. Therefore, we **fail to reject the null hypothesis** that the series is white noise at the 95% confidence level. ### Key Points: - The Ljung-Box test is generally preferred over Box-Pierce for smaller samples as it has better small-sample properties - Both tests indicate the same conclusion in this case - "Accepting white noise" technically means we fail to find sufficient evidence against the null hypothesis **Conclusion**: With 95% confidence, we fail to reject the null hypothesis that the series is white noise.
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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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