Time Series Online Prediction Based On Kernel Adaptive Filter

Multivariate time series exists in various fields,including hydrology,meteorology,transportation,and medical treatment.Prediction and analysis of these time series are of great significance in guiding the life and production of human society.In addition,in many systems,the characteristics of time series are complex and time varying,and the data size of time series is increasing day by day.Therefore,it is urgent to develop appropriate time series online prediction methods.In this paper,we study multivariate time series online prediction based on a kernel adaptive filter(KAF).For the multivariate time series with time varying characteristics and large data volume,appropriate online prediction methods are designed to improve the prediction efficiency and accuracy and enhance online prediction ability.First,the computational complexity of the kernel recursive least square(KRLS),which is a representative method of kernel adaptive filters,is increased with the increase of sample size,and it is sensitive to environmental noise.Therefore,the adaptive normalized sparse kernel recursive least squares(ANS-KRLS)method is proposed.In this method,approximate linear dependency(ALD)and coherence strategies are used to judge the selection of the new samples,and only those with larger contribution to online prediction will be retained.Through this sparsification idea,the dimension of the kernel matrix is reduced and the prediction efficiency is improved.In addition,the normalization idea is added to realize the adaptive dynamic adjustment of the coefficients in the update process,and then the noise immunity of the method is enhanced.Second,when using sparse strategies to improve KRLS,the inputs that are judged to be redundant will be discarded directly,which may cause some useful information to be lost.Therefore,the adaptive normalized sparse quantized kernel recursive least squares(ANS-QKRLS)is proposed.In this method,online vector quantization is added while performing sparse processing,which uses the redundant information to update the coefficients.And it continues the previously mentioned adaptive dynamic adjustment strategy to improve the prediction accuracy and efficiency.Finally,to solve the problem of unsatisfactory ability to track the time varying characteristics of time series for KRLS,a sparse kernel recursive least squares based on sliding window(SW-SKRLS)is proposed.The sliding window is added to sparse KRLS,which considers the time varying factors while limiting the dimensions of the kernel matrix.In this process,the members in the sample dictionary are properly deleted to enhance the ability of the method to track the time varying characteristics of the time series.In addition,neural network methods have good nonlinear fitting ability,and it can be complemented with the advantages of the global optimality of the kernel adaptive filter methods.Therefore,the extreme learning machine(ELM)method and the KRLS method are linked together.And then,learn from the idea of SW-SKRLS,a sparse kernel online sequential ELM with sliding window(SWS-KOS-ELM)is proposed.In this paper,the simulation results of the El Nino-Southern Oscillation(ENSO)related index time series,Lorenz time series,the sunspots and Yellow River annual runoff time series,and Dalian meteorological data are used to verify the effectiveness of the proposed methods.