Testing for randomness against autocorrelation: Alternative tests

Abstract

The asymptotic efficiencies of the rank serial correlation and turning–points tests with respect to the serial correlation test are evaluated for first–order autocorrelation. Tests based on the periodogram of the data are suggested. A Monte Carlo study is conducted to evaluate the relative performance of likelihood derivative, distribution–free, and periodogram tests for small to moderate sample sizes with normal and nonnormal parent distributions. The serial correlation test and a Kolmogorov–Smirnov test based on the periodogram are generally recommended.