Dynamical models of high-frequency data analysis

To treat with social phenomena, statistical and mathematical physics provides a powerful and rigorous method [1], and several papers have studied the models of social phenomena based on stochastic processes. Many researchers in econometrics or biometrics have proposed that the discrete choice including binary analysis may be formulated as the AR (autoregressive), logit, and probit models [2]. In this paper, we present the future predictability of the AR and logit models, by using the tick data analysis of the KOSPI. We consider two delivery periods of the KOSPI: Data A (B) was from January 1997 to December 1998 (January 2004 to December 2004). Data A (B) contains 133,823 (86,561) items of minutely data. In our calculations, to determine the minimized order k of AR and logit models, we define the Akaike information criterion (AIC) as AIC = 2 T [− lnMl + lnMp] for the sample size