Multivariate Time Series Segmentation And Prediction Approach And Application Research

With the deepening and development of the research on the issues related to time series,it is becoming more important to study multiple time series with correlation among them,namely,multivariate time series analysis.This thesis investigates the problems of multivariate time series segmentation and prediction,and the research mainly includes the following topics:(1)The thesis proposes a multivariate time series segmentation approach based on dynamic programming algorithm.According to the definition of segmentation cost,the proposed seg-mentation approach automatically segments time series using dynamic programming algorithm,and the obtained segmentation result is the global optimum segmentation.In this segmentation approach,the definition of segment errors of multivariate time series is given first,and the re-cursive formulation of segment errors that can effectively reduce the computational complexity is also developed.The calculation of segment errors is based on vector autoregressive models,and the order of autoregression and segmentation are simultaneously determined by Schwarz's Bayesian information criterion.In the experiments,both simulation data and hydrometeorologi-cal multivariate time series are used to evaluate the performance of the proposed algorithm.The experimental results show that the proposed algorithm performs well.(2)This study proposes a segmentation algorithm to partition time series,where fuzzy clus-tering is realized for the time series segments formed in this way.The segmentation approach involves a new objective function,which incorporates an extra variable related to segmentation,while dynamic time warping is applied to determine distances between nonequal-length series.To optimize the introduced objective function,we put forward an effective approach using dy-namic programming algorithm.When calculate the dynamic time warping distance,a dynamic programming-based technique is developed to reduce the computational complexity.In a series of experiments,both synthetic and real-world time series are used to evaluate the performance of the proposed algorithm.The results demonstrate higher effectiveness and advantages of the constructed algorithm when compared with the existing segmentation approaches.(3)A hybrid model of vector autoregressive moving average(VARMA)models and Bayesian networks is proposed to improve the forecasting performance of VARMA models for multivariate time series.In the proposed model,the VARMA model,which is a popular linear model in time series forecasting,is specified to capture the linear characteristics.Then the errors of the VARMA model are clustered into some trends by K-means algorithm with Krzanowski-Lai cluster validity index determining the number of trends,and a Bayesian network is built to learn the relationship between the data and the trend of its corresponding VARMA error.Fi-nally,the estimated values of the VARMA model are compensated by the probabilities of their corresponding VARMA errors in each trend,which are obtained from the Bayesian network.Compared with VARMA models,the experimental results with two multivariate real-world data sets indicate that the proposed model can effectively improve the prediction performance.(4)This thesis proposes a time series long-term prediction approach based on hidden Markov models.Following the principle of justifiable granularity,the original numerical da-ta is transformed into some meaningful and interpretable sequences.The obtained sequences exhibiting an essential semantics may have different lengths,which will bring some difficulties when carry out predictions.To equalize these temporal sequences,we propose to adjust their lengths by involving the dynamic time warping distance.Two theorems are included to ensure the correctness of the proposed equalization approach.Finally,we exploit hidden Markov mod-els to derive the relations existing in the granular time series and produce long-term prediction.A series of experiments using publicly available data are conducted to assess the performance of the proposed prediction method.The comparative analysis demonstrates that proposed approach performs well.