Frequency analysis of tick quotes on foreign currency markets and the double-threshold agent model

Power spectrum densities for the number of tick quotes per minute (market activity) on three currency markets (USD/JPY, EUR/USD, and JPY/EUR) are analyzed for periods from January 2000 to December 2000. We find some peaks on the power spectrum densities at a few minutes. We develop the double-threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision-making of them. This model is numerically performed and theoretically investigated by utilizing the mean-field approximation. We propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants.