Optimal Range for the iid Test Based on Integration Across the Correlation Integral

This paper builds on Kocenda (2001) and extends it in three ways. First, new intervals of the proximity parameter ε (over which the correlation integral is calculated) are specified. For these ε-ranges new critical values for various lengths of the data sets are introduced, and through Monte Carlo studies it is shown that within new ε-ranges the test is even more powerful than within the original ε-range. The range that maximizes the power of the test is suggested as the optimal range. Second, an extensive comparison with existing results of the controlled competition of Barnett et al. (1997) as well as broad power tests on various nonlinear and chaotic data are provided. Test performance with real (exchange rate) data is provided as well. The results of the comparison strongly favor our robust procedure and confirm the ability of the test in finding nonlinear dependencies as well its function as a specification test. Finally, new user-friendly and fast software is introduced.