Abstract
In this article, we looked at power of various versions of Box and Pierce statistic and Cramer von Mises test. An extensive simulation study has been conducted to compare the power of these tests. Algorithms have been provided for the power calculations and comparison has also been made between the semi parametric bootstrap methods used for time series. Results show that Box-Pierce statistic and its various versions have good power against linear time series models but poor power against non linear models while situation reverses for Cramer von Mises test. Moreover, we found that dynamic bootstrap method is better than xed design bootstrap method.
Highlights
Time series model building is a science and art as well
Our results show that Box-Pierce type tests do well against the linear alternatives but fail to perform against the non-linear alternatives, while the situation reverses for the Cramer von Mises (CvM) statistic due to Escanciano (2007), i.e, the CvM statistic does well against various non linear alternatives but much less well against various linear alternatives
We present and compare the power against linear and non-linear alternative class of models under a linear null model
Summary
Time series model building is a science and art as well. It is generally considered a three stage iterative procedure consisting of identification, estimation and diagnostic checking (Box and Jenkins, 2008). Box and Pierce (1970) test and its several other versions are perhaps the most commonly used types of portmanteau test (Mainassara et al, 2009). These tests are capable to perform an overall test for an entire set of, say, the first m autocorrelations assuming that the null model, i.e. the model defined under null hypothesis, is correct. The choice of m is very important in the appropriateness of asymptotic distribution and power of these tests
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