A study on transaction volumes and intervals in the financial market and its applications

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The empirical analysis on the tick data of the Osaka Securities Exchange shows that the transaction intervals are best described by the Pareto distribution of Type III if the observation period is 15 minutes. The volume of one transaction is best described by the negative binomial distribution. The parameters depend regularly on time so that one must be careful if he/she needs a model for the whole day.The Japanese proverb says that financial markets are bullish when the available liquidity on the ask side is deeper. Theoretical and empirical analysis shows that the results depend on the assumptions of the model in the theoretical case, and depend on the details of measurement methods in the empirical case. The proverb is sometimes correct, and sometimes not.