Distribution-Free Tests in Time-Series Based on the Breaking of Records

Abstract

Summary Two simple statistics are proposed as distribution-free tests of the randomness of a series of observations. They are linear functions of the numbers of upper and lower records which occur in the series. They are uncorrelated and asymptotically normally distributed. One provides a consistent test against trend in the mean and the other a consistent test against trend in the variance. Power functions for the former test have been computed, and it is pointed out that this test is considerably more powerful than three well-known tests. It is not as powerful as the rank-correlation tests, but is on the other hand very much simpler to compute. Illustrative applications are made to data from meteorology and athletics.