Generalized beta distributions for describing and analysing intraday stock market data: testing the U-shape pattern

There is an impressive body of empirical evidence which indicates the existence of an intraday U-shaped curve in stock prices. In an effort to shed additional light on the U-shaped curve a new procedure for U-shape testing is introduced. From careful analysis of intraday data it is observed that minimum or maximum stock prices can occur several times during the day. Here, attention is focused on the first time during the day that the maximum or minimum stock price occurred. Because of the importance of the first time during the day that the maximum or minimum stock price occurred, an attempt is made to model these two characteristics with probability distributions. The objective of this study is to use a generalized beta distribution to examine the intradaily behaviour of stocks, using closing stock prices for each one-minute interval, using data from Athens Stock Exchange (ASE). This generalized beta distribution has not been used before to model U-shaped behaviour. The results are consistent with the intraday U-shaped curves, i.e. the time to first maximum (or minimum) stock prices follows a U-shaped pattern. In addition, some potential applications of the generalized beta distribution are discussed and exemplified by analysing the relationship between herd behaviour and U-shaped.