Nonlinear Time Series Prediction,analysis And Anomaly Detection

Non linear and non-stationary time series is one of the most common types of time series in our real life.As a non-stationary and non-linear time series reflecting the price changes of the stock market in the financial market,the stock price index series is of great significance for the study of the stock market.The purpose of this paper is to explore the inherent properties of the stock price index and the applicable forecasting methods.The first part of this paper is the research of several nonlinear time series prediction methods.Based on the correlation characteristics of stock series,a novel two-stage hybrid model EEMD-FFH(Ensemble empirical mode decomposition-Fractional frequency hy-brid)is proposed to predict the future stock index according to the historical stock index.And the W-E distance is proposed to improve the matching performance of the model.Finally,EEMD-FFH is compared with other methods on various data sets to verify its robustness.The second part of this paper mainly explores the applicability of deep learning method in the field of nonlinear time series prediction.In this part,the deep learning Recurrent neural network(RNN)and its improved methods,Long-term and short-term memory artificial neural network(LSTM)and Gated cyclic unit recurrent neural network(GRU),are used to predict the stock index,and the results are compared with those of EEMD-FFH.In the third part of this paper,on the basis of EEMD-FFH algorithm,the predictabil-ity measure based on information theory and the prediction accuracy in the field of se-quence prediction are linked for the first time,and explore the relationship between the predictability of stock prices at different sampling frequencies and the prediction accu-racy of the algorithm.The topic in this part is whether the stock sampling frequency af-fects its predictability and the prediction accuracy of EEMD-FFH algorithm,and whether the predictability of the series is positively related to the real prediction accuracy.The experiments results on SSE50 index data set are consistent with intuition.In the fourth part of this paper,an effective anomaly detection method based on Ma-halanobis distance(AKM D)is introduced,and the kernel technique is introduced.In order to describe the dynamic of the process,the data is augmented,and the derivation proves that this processing can effectively improve the detection efficiency.In the ex-perimental part,a complex nonlinear dynamic system is simulated,and three fault types are set for data interference.Five detection indexes are used for experiments,including T~2and SP E,Euclidean distance(ED),Mahalanobis distance(M D)and AKM D.The results show that AKM D has the highest detection accuracy for each type of fault.