On the predictability of high-frequency financial time series

Abstract

We focus on the memory length and its stability of the tick-wise price, fluctuations. It is known that the price fluctuations can be approximated by the random walk but has a short memory. However it has not been known so far what exactly the memory length is and how stable it is. We have analyzed tick-wise price fluctuations of U. S. Dollar vs. Japanese Yen exchange rates extending for five and a half years, by automatically generating the output files of conditional probabilities for the memory length up to seven. We have identified the memory length be three ticks almost everywhere throughout the entire period of the data. This result coincides with two other independent analyses; autocorrelation functions and mutual informations. This fact implies a possibility of short time prediction based on Markov type models.