Stationary Process and Ergodicity

Zhaodong Wang and Weian Zheng

Chapter 5 in High-Frequency Trading and Probability Theory, 2014, pp 85-108 from World Scientific Publishing Co. Pte. Ltd.

Abstract: We find that the high-frequency trading (HFT) is closely related to the ergodic theory of stationary processes [12]. As we have shown in the previous chapters, in most HFT cases, the trader cannot guarantee to make profit in each of his trades. However, if a trader can repeatedly apply the same algorithm with positive expected profit to trade, then the strong ergodic theorem will lead to a steadily increasing accumulated profit as the total sum, if the profit series forms an ergodic stationary time series. That is the main thing we will explain in the next four chapters…

Keywords: High-Frequency Trading; Algorithm Trading; Program Trading; Technical Analysis (search for similar items in EconPapers)
Date: 2014
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