Modelling high-frequency economic time series

The minute-by-minute move of the Hang Seng index (HSI) data over a 4-yr period is analyzed and shown to possess similar statistical features as those of other markets. Based on a mathematical theorem, we derive an analytic form for the probability distribution function (PDF) of index moves from fitted functional forms of certain conditional averages of the time series. Furthermore, following a recent work by Stolovitzky and Ching, we show that the observed PDF can be reproduced by a Langevin process with a move-dependent noise amplitude. The form of the Langevin equation can be determined directly from the market data.