Modelling high-frequency economic time series

The minute-by-minute move of the Hang Seng index (HSI) data over a 4-yr period is analysed and shown to possess similar statistical features as those of other markets. Based on a mathematical theorem (Pope, Ching, Phys. Fluids A 5 (1993) 1529), 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 (Phys. Lett. A 255 (1999) 11), 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