Question

Explain the limitations of (i) Variance Ratio test, and (ii) Box-Pierce Q test  in assessing the concept of market efficiency.

Answer 1

Limitation of Various Concept :

(1)Variance Ratio test :

• limited to the study of observations drawn from contaminated normal distributions, both because such distributions are common in practice and because they cannot be readily transformed.
• is designed to test against any and all alternatives to the null hypothesis and thus may be suboptimal for testing against a specific hypothesis.
• It assume the dataset is uniformly distributed with means of each sub-set data group to be equal. Similarly, the variance and standard deviation of each sub-set data group is equal.

(2)Box-Pierce Q test :

• The null hypothesis of the Box Ljung Test, H0, is that our model does not show lack of fit (or in simple terms—the model is just fine). The alternate hypothesis, Ha, is just that the model does show a lack of fit.
• A significant p-value in this test rejects the null hypothesis that the time series isn’t autocorrelated.

• The Box-Pierce test uses the test statistic, in the notation outlined above, given by[1]

  {\displaystyle Q_{\text{BP}}=n\sum _{k=1}^{h}{\hat {\rho }}_{k}^{2},}

  and it uses the same critical region as defined above.

  Simulation studies have shown that the distribution for the Ljung–Box statistic is closer to a {\displaystyle \chi _{(h)}^{2}} distribution than is the distribution for the Box-Pierce statistic for all sample sizes including small ones. which can be not used for big market size.