Deviation Analysis And Complexity Measurement For Non-stationary Time Series

In recent years,the study of deviation and complexity of non-stationary time series has received more and more attention.The corresponding models and methods have been widely used in economics,physiology,sociology and other fields.This paper proposes several new methods for measuring the deviation and complexity of time series,and applies these models to time series such as finance and physiology.This paper first proposes a generalized deviation model.The generalized deviation model can not only study the correlation between historical stock returns and future volatility of financial time series,but also study the degree of deviationand amplitude size of different stock indexes and individual stocks.First we simulate the actual sequence and study the relationship between historical stock price and future volatility through ARMA sequences and ARFIMA sequences.The rigor and accuracy of the model was then demonstrated using global stock indices and US stock data in the actual financial markets.For the experimental data results,the exponential function is used for fitting,and the generalized deviation analysis model is used to quantify and analyze the volatility results.After that,the model is quantitatively analyzed,and the time period of the historical price data points is divided to obtain the difference between different time periods.Then the difference and relationship between the price volatility during the financial crisis and the volatility between the non-financial crises are obtained.In addition,we will conduct further research on deviation and study the relationship of volatility on negative definitions.Secondly,this paper also proposes a new method to study the complexity of time series-multi-scale Tsallis permutation entropy analysis.The model was improved on the basis of Shannon entropy.Compared with Shannon entropy,Tsallis permutation entropy pays more attention to the correlation for Hurst index.The selections of embedding dimensions and delay times also have crucial impacts on the complexity research of the sequence.We first use the AR model sequence to verify the validity of this model.The ECG time series(ECG)of people in different health conditions were then subjected to multi-scale analysis and the differences in ECG sequences between healthy and disease patients were studied.The corresponding numerical results also portray the effectiveness of the proposed maximum entropy principle based on the negative Tsallis entropy index.Finally,based on the complexity analysis,we construct a ordinal matrix model under different dynamic systems and judge the classification of non-stationary time series by the number of sequential matrices,including periodic sequences,quasi-periodic sequences,chaotic sequences and random sequence.Then,by constructing the form of the multivariate function,the minimum mean square error is fitted to the number of sequential matrices.And then get the optimal number of order matrices under different orders.Corresponding experimental results can help us provide effective reference and decision making for studying non-stationary sequences under different systems.