A New Test for Randomness with Application to Stock Market Index Data

Strandberg and Iglewicz (2012) propose a test that detects deviations from randomness, without an a priori distributional assumption. This nonparametric test is designed to detect deviations of neighboring observations from randomness, especially when the dataset consists of time series observations. The proposed test is especially effective for larger datasets. In our simulation study, this test is compared to a number of variance ratio and traditional statistical tests. The proposed test is shown to be a competitive alternative for a diverse choice of distributions and data models. In addition, this test is able to successfully detect changes in variance, which can be informative in short term investing and option trading. In our empirical application, we review and compare several transformations while evaluating common US stock market indices. We consider two commonly used transformations and a proposed new transformation from Strandberg and Iglewicz (2012). This new transformation performs surprising well for stock market index data and is the only transformation to show consistence results among the considered tests.