Causality Analysis Of Nonlinear Time Series On Multiple Time Scales

There is a complex nonlinear interaction between participating entities and their influence factors in the stock market,thus realizing information interaction,flow,feedback,restriction and other behaviors.The structural and evolutional information of stock market can be reflected by the price fluctuation of stock,and the price fluctuation of stock mostly has complex non-linear as well as non-stationary characteristics,which leads to the failure of traditional linear analysis method.As a main participant in the stock market,investors are the key factors to determine the evolution of the stock market and stock price fluctuation.The limited attention of investors is an significant way to obtain investment information and it reflects the attention of investors to the stock market,which is considered as an important branch of behavioral finance theory.At present,it's the traditional econometric model that is generally used to study the relationship between stock prices and investors' attention,and only on one single scale.Therefore,it is an urgent problem to explore the causality on multiple scales between stock price fluctuations and investor's attentions.In this paper,an adaptive data-driven analysis method:Ensemble Empirical Mode Decomposition(EEMD),is introduced into the study.First,we construct the proxy variables of investors' attention by Baidu Index.Second,from the perspective of multi-scale analysis,EEMD method is applied to decompose the stock price time series and Baidu Index time series into several independent,different intrinsic mode functions and one residual term,extracting the fluctuation characteristics of the original time series on different time scales.Third,according to the frequency of the basic intrinsic mode functions,they are divided into high frequency components,low frequency components and an residual term,which represent the short-term fluctuation,the medium-term trend and the long-term trend respectively.Fourth,based on EEMD,the multi-scale Granger causality test model and the multi-scale symbolic transfer entropy method are constructed.Finally,the individual stocks in China's stock market are divided by the stock value.The multi-scale causality analysis between stock prices of different value and investors'attention is studied systematically.The empirical results show that in China's stock market,the causality relationship between stock price fluctuations and investors' attention is various on different time scales.This kind of causality is distinct between large-cap stocks and small-cap stocks.In the short term,both for large cap stocks and small cap stocks,there are information flows on different directions between stock prices and investors' attention,that is,they show the reciprocal causality;in the medium term,there is no causality between the price fluctuations of large-cap stocks and the change of Baidu Index,while for small-cap stocks,the the stock price fluctuations and the change of Baidu Index show reciprocal causality for each other;in the long term trend,there is no causality between the fluctuation of stock prices and the change of Baidu Index.On this point,both large-cap stocks and small-cap stocks perform the same.