A Nonparametric Test for Deviation from Randomness with Applications to Stock Market Index Data

Abstract

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 dataset consists of time series observations. Simulation results and a comparison with Lo and MacKinlay's (1988) variance ratio test showed that our proposed test is a competitive alternative.

Keywords:

• Binomial
• Percentiles
• Time series
• Tukey's g-and-h distributions
• Variance ratio tests

Mathematics Subject Classification:

• 62G10

Acknowledgment

The authors wish to thank the reviewers and editor for their very helpful suggestions that improved the article.