Abstract
It is well known that the price time series of an efficient market display a Brownian motion. In such a case the best prediction of a future price is the last-known price thus no arbitrage is possible. A real market is, however, possibly not perfectly efficient. In this paper, we apply an error back-propagation neural network to tick-by-tick high-frequency time series of Chinese A-share stock prices and try to predict their future values. The performance of the predictions varies largely for different stocks. In order to seek for the dependence of the performance, we study the long-range correlation (LRC) of the data by the conventional detrended fluctuation analysis (DFA) and its generalization, the multifractal detrended fluctuation analysis (MFDFA). Clear relevance between the performance and the LRC is observed. The prediction is particularly good when the time series are strongly anti-persistent.
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