Non-linear time series invariants to study price manipulation in stock market

Abstract

Several studies have found the successive prices at which trades of shares are executed in a stock exchange to form time series with non-linear characteristics. Invariants of a non-linear time series of share prices contain valuable information about the patterns in the share prices, which factor may be useful in the analysis of share prices for various purposes. Of the commonly used invariants, entropy is found to be a useful tool in studying price manipulation in stock market. Among the various versions of entropy, sample entropy computed for the price data of a share, for various trading days in the period during which the share was reported to be subject to price manipulation, proves to be potential evidence for manipulation of the share's price. This paper studies the suitability of sample entropy of non-linear time series of share prices and also the selection of appropriate values for the parameters used for computation of sample entropy of a short time series of share prices, for investigating into price manipulation in stock market.