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Testing autocorrelation in the residuals is a standard specification check applied after fitting an ARMA model. There are two closely related tests in this specification analysis, namely the Box-Pierce test and Ljung-Box test. Which of the following statements correctly distinguishes these two tests?
A
They share the same null hypothesis, which states that at least one autocorrelation is non-zero.
B
The Box-Pierce test works better in smaller samples compared to the Ljung-Box test.
C
Asymptotically, the Box-Pierce test-statistic follows a chi-squared distribution, while the Ljung-Box test-statistic follows a Levy distribution.
D
Under both tests, a rejection of the null hypothesis implies that the model fails to capture some dynamics in a time series.