Ensemble Kernel Learning Model for Prediction of Time Series Based on the Support Vector Regression and Meta Heuristic Search

In this paper, a method for predicting time series is presented. Time series prediction is a process which predicted future system values based on information obtained from past and present data points. Time series prediction models are widely used in various fields of engineering, economics, etc. The main purpose of using different models for time series prediction is to make the forecast with the greatest accuracy. The model presented in this paper is based on the combination of kernels and support vector regression. Support vector regression is highly capable of solving function estimation problems by using its kernels, but kernels’ parameters need to be adjusted. First we have preprocessing phase which includes normalizing data and separating data for testing and training. In proposed model, ten different kernels were used. Five kernels were selected as the best kernels by trial and error and these kernels are applied to data. There may be only a few of the kernels that are useful for the problem, and we are not aware of which kernels are useful for our problem so kernel outputs aggregate by applying a coefficient. This combination creates a new secondary space. The output is given to support vector regression to construct a model that predicts values exactly ɛ accurate, which means the predicted values do not deviate more than ɛ from the original data. This model predicts values by using a leave one out model. Each kernel has parameters that need to be set to optimum values in order to get the best results. Hence in the proposed model, the kernel parameters and their weights are learned by the Gray Wolf Optimizer. This optimizer has been able to provide appropriate answers to many problems, especially challenging problems and has a superior ability to solve the high-dimension problems. By running program in consecutive iterations and examining the different values of the parameters, the optimizer learns the best of them which prediction error has been reduced, and finally returns their best value. The proposed model is implemented on five standard time series and compared to other method, test based on the RMSE criterion for DJ time series, improved by 1.58 point, Radio time series, improved by 0.178 point, and Sunspot time series, improved by 1.709 point. Finally, we analyzed the results, Statistical evaluation by Wilcoxon Signed-Rank Test where the p value is very low compared to the proposed method and CNN-FCM, AR_ model per scale, Multiresolution AR model and ANN methods, slightly lower for Wavelet-HFCM and ANFIS methods and slightly lower than one for SAE-FCM method and at the end provide a relation to find the window size in the model by obtaining the average of peak differences, valley differences, and consecutive peak and valley differences for the actual values of the training data in exchange for their sequence number in time series.