A Nonparametric Test for Deviation from Randomness

Abstract

There are many existing tests used to determine if a series consists of a random sample. Often these tests have restrictive distributional assumptions, size distortions, or low power for key useful alternative situations. The interest of this dissertation lies in developing an alternative nonparametric test to determine whether a series consists of a random sample. The proposed test detects deviations from randomness, without a priori distributional assumption, when observations are not independent and identically distributed (i.i.d.), which is suitable for our motivating stock market index data. Departures from i.i.d. are tested by subdividing data into subintervals and then using a conditional probability measure within intervals as a binomial test. This nonparametric test is designed to detect deviations of neighboring observations from randomness when the data set consists of time series observations. Simulation results confirm correct test size for varied distributions and good power for detecting alternative cases. This test is compared to a number of other popular methods and shown to be a competitive alternative. Although the proposed test may be applicable to multiple areas, this dissertation is mostly interested in applications to stock market and regression data. The proposed test is effectively illustrated with the common three stock market index data sets using a newly created transformation, and shown to perform exceptionally well.