Financial Risk Manager Part 1
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The Box Pierce and the Ljung Box Q-statistics are used to measure the degree to which autocorrelations vary from zero and to establish whether white noise might be present in a set of data. Which of the following statements is incorrect regarding these two test statistics?
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NNikitesh
A
The Box Pierce test has better small sample properties compared to the Ljung Box test
B
Asymptotically (as the sample size increases), the values of the two test statistics will be equal
C
The Box Pierce test is sometimes oversized for small samples
D
Both tests show a tendency to reject the null hypothesis of zero autocorrelations as n tends towards infinity
Explanation:
The Ljung Box test was developed in part because the Box Pierce test is sometimes oversized for small samples. Thus, the Box Pierce test will tend to reject the null hypothesis of zero autocorrelation more frequently than it should at a certain level of confidence. For example, if the level of significance is 10%, the test statistic will lead to the rejection of H₀ more than 10% of the time.
Key Points:
- Statement A is incorrect because the Ljung Box test actually has better small sample properties than the Box Pierce test.
- Statement B is correct - asymptotically, both test statistics converge to the same distribution.
- Statement C is correct - the Box Pierce test is known to be oversized (over-rejective) for small samples.
- Statement D is correct - as sample size increases, both tests become more powerful and tend to reject the null hypothesis more frequently.
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