Research On The Uncertainty And Prediction Of Financial Time Series

The research on the uncertainty and prediction of time series has attracted more and more attention from researchers in various disciplines,and various analytical research methods have also been widely used in medical,physics,economics,and biological sciences.This paper proposes two measurement methods for the uncertainty study of time series,and a prediction method for time series,and takes financial time series as the research object.First,based on the Havrda-Charvat entropy of the permutation mode,in order to mine different amplitudes under the same permutation mode,a new entropy method—weighted Havrda-Charvat entropy is proposed.To analyze the practicability of this method,we study seven sets of time series,including a logistic mapping as simulated data,and three kinds of stock data of China and the United States,respectively,as financial data,namely Chinese Shanghai Stock Index,Shenzhen Component Index,and Shanghai and Shenzhen 300 Index,as well as the US S&P500,Nasdaq and Dow Jones Industrial Index.By comparing the effects of different embedding dimensions,degree of coarse graining,and weight on the time series,we can analyze that the entropy value decreases as the degree of coarse graining increases,and tends to be stable.For the embedding dimension,the entropy value is significantly different when the embedding dimension is higher,which is more conducive to our analysis of the uncertainty changes in the time series.In addition,although the weighted Havrda-Charvat entropy maintains similarity with Havrda-Charvat entropy in trend,it is always lower than Havrda-Charvat entropy in value and fluctuates in a small range.Under the effect of weight,the entropy value of Havrda-Charvat entropy decreases,indicating that the uncertainty of the time series has decreased,and it also shows that the weight has a good effect on the measurement of the uncertainty of the time series.Secondly,by analyzing the application of permutation entropy and distribution entropy on simulated data,we find that the two entropy methods have advantages and disadvantages in different time series.Therefore,we propose a two-dimensional entropy plane based on permutation entropy and distribution entropy.So that the two entropy methods can achieve complementary effects,and it can be applied to a variety of time series.At the same time,in view of the good performance of Havrda-Charvat entropy in financial time series,we propose a two-dimensional entropy plane formed by permutation Havrda-Charvat entropy-distribution Havrda-Charvat entropy.First,we verify the feasibility of the two-dimensional entropy plane formed by the permutation HavrdaCharvat entropy-distribution Havrda-Charvat entropy on the simulated data-logistic mapping,and then we pass the experimental analysis on the stock data of Asia,America and Europe.The data are Asian Shanghai Stock Index,Hong Kong Hang Seng Index,Nikkei 225 Index;American Dow Jones Industrial Index,Nasdaq Index,S&P 500 Index;and European Dutch AEX Composite Index,French CAC40 Index,Spanish IBEX Index.We can find that the stock data of the Americas is relatively concentrated and easy to distinguish.Japanese stock data in Asia is closer to American and European stock indexes than Chinese.The European stock data is relatively scattered and matches the economic differences of countries on the entropy plane.This shows that the replacement of the entropy plane formed by permutation Havrda-Charvat entropy-distribution HavrdaCharvat entropy can better describe the similarity,randomness and uncertainty of time series.Finally,this paper also proposes a generalized k-nearest neighbor-invariant time series forecasting method.In order to solve the three problems of k nearest neighbor: amplitude and offset invariance,complexity invariance and trivial matching,we propose normalization and complexity invariant distance.At the same time,in order to make k nearest neighbors applicable to multiple time series,we generalize the complexity invariant distance,and propose a generalized k nearest neighbor-invariant time series forecasting method.Through simulation experiments on the ARFIMA model,it is verified that the prediction method can be more effectively used to improve the accuracy of prediction.Afterwards,the Shanghai Stock Index and the Nasdaq index are used as references to select the best generalized k-nearest neighbor-invariant time series forecasting methods;at the same time by seven other stock markets in Asia,Europe and the United States-Hong Kong Hang Seng Index,Nikkei 225 index,Dow Jones Industrial Index,S&P 500 index,the Dutch AEX composite index,the French CAC40 index,and the Spanish IBEX index,we verify that the generalized k nearest neighbor—a time series forecasting method with invariance has practical application value in financial time series forecasting.