Dynamical Structures of High-Frequency Financial Data

We study the dynamical behavior for high-frequency data of the Korean stock price index (KOSPI) using the movement of returns in Korean financial markets. It is shown that the dynamical behavior for a binarized series of our models is not completely random. The conditional probability are numerically estimated from a return series of tick data in the KOSPI. Non-trivial probability structures can be constituted from binary time series of the autoregressive (AR), logit, and probit models for which the Akaike Information Criterion (IC) value shows a minimum value at the $15$th-order. From our result, the value of correct match ratio for the AR model is found to relatively have slightly larger than calculated findings of other models.