A Test for Iid Residuals Based on Integrating Over the Correlation Integral

Abstract

This paper presents a new method of testing for IID. The test is suggested as an alternative to the nonparametric BDS test, which requires a proximity parameter (and an embedding dimension m to be chosen arbitrarily. A limited statistical theory exists to determine the right choice of these parameters. The presented method aims to eliminate such indecisiveness by integration over the correlation integral. The Monte Carlo simulation is used to tabulate critical values of the new statistic. In a comparative analysis the presented test is able to find nonlinear dependencies in cases where the BDS test does not find them. The test becomes more critical to the question whether the data is true white noise.