Extracting The Trends Of Time Series Based On The Copular Functions

In this paper,we discuss the use of dynamical systems methods to study non-linear time series prediction problem,and especially have an innovation in extracting the trends of time series methodologically.The object we concern here is a complex system of the U.S.stock market,by using the time series observations of Standard & Poor and NASDAQ index,in order to find the function relationship of the complex system.First of all,we use Copula function to structure a measure model and extract the trends of time series,and then with the trends of time series data of the complexity of the system to find the function relationship hidden in it.When searching for the relationship of the stock market,we demonstrate the United States stock market is a complex system with Chaotic characteristics,ultimately we determine to use the method of dynamical system for the short-term prediction of the stock market index.There are four parts in this paper:1.The introduction of Copula functions,including the definition of Copula functions and empirical Copula functions,and the theorem of Sklar.2.We make use of Copula function method in this paper to structure a measure model to extract the trend of time series.3.In order to study the complex system of the U.S.stock market,it is bound to find the functions of internal relations which the system contains.Using the data of observation time series of Standard & Poor and the NASDAQ index,we make a prediction of the trends of the time series by linear and piecewise linear methods,and the results show that the time series come from a complex system which has chaotic non-linear characteristics.4.This chapter is the core of the paper.As knowing the fact that the U.S.stock market has chaotic characteristics,we make a discussion by using the dynamical system method.Through makingthe phase space reconstruction of time series of two-dimensional complex system,we can find the function relationship hidden within it at last,and make a better short-term forecast.5.In this chapter we make the conclusions including extracting time series trends by using the integral absolute error structure model with Copula functions is proved better;the U.S. stock market is a nonlinear system with chaotic characteristics,it is a more effective approach for short-term prediction by the dynamic system method.