Long Memory Analysis And Episodic Modeling Based On Trade Data

In stock market long memory is generally considered as the long dependence of the financial time series. Log-returns are supposed to be independently and identically distributed in current financial theory which does not include long memory. So the existence of long memory in stock market will make a great influence on the current financial theory.The episodic memory is the memory of event or scene that someone has experienced personally in a certain time and location. Researches on episodic memory show that people guide their memories by the profound events.To study long memory and episodic modeling based on trade data, researches in this paper are as follows:Firstly, the methods of testing long memory are studied. By simulation, it is found that short memory in time series will make a large error between estimated value by R/S analysis method and real value. A new method is constructed for estimating the long memory parameter based on the autocorrelation function or the partial autocorrelation function. Different methods are used to test the daily log-returns of Shanghai and Shenzhen index. The results show that the daily log-returns almost do not include long memory, but the absolute daily log-returns include evident long memory.Secondly, the steps of using ARFIMA model to analyze long memory time series are summarized. The forecasting formulas of ARFIMA model are provided and their properties are also presented.Thirdly, an episodic memory system is established based on the trade data. A calculation example of the model is presented based on the study of event patterns on trade data. The actual data analysis shows that the episodic memory model allows the system to search its historical memory episodes according to the current states and thus make certain judgments for the current situation.