This study proposes two metrics using the nearest neighbors method to improve the accuracy of time-series forecasting. These two metrics can be treated as a hybrid forecasting approach to combine linear and non-linear forecasting techniques. One metric redefines the distance in k-nearest neighbors based on the coefficients of autoregression (AR) in time series. Meanwhile, an improvement to Kulesh's adaptive metrics in the nearest neighbors is also presented. To evaluate the performance of the two proposed metrics, three types of time-series data, namely deterministic synthetic data, chaotic time-series data and real time-series data, are predicted. Experimental results show the superiority of the proposed AR-enhanced k-nearest neighbors methods to the traditional k-nearest neighbors metric and Kulesh's adaptive metrics.
This study presents a time series prediction model with output self feedback which is implemented based on online sequential extreme learning machine. The output variables derived from multilayer perception can feedback to the network input layer to create a temporal relation between the current node inputs and the lagged node outputs while overcoming the limitation of memory which is a vital port for any time-series prediction application. The model can overcome the static prediction problem with most time series prediction models and can effectively cope with the dynamic properties of time series data. A linear and a nonlinear forecasting algorithms based on online extreme learning machine are proposed to implement the output feedback forecasting model. They are both recursive estimator and have two distinct phases： Predict and Update. The proposed model was tested against different kinds of time series data and the results indicate that the model outperforms the original static model without feedback.
