Residuals-based deep least square support vector machine with redundancy test based model selection to predict time series

In this paper, we propose a novel Residuals-Based Deep Least Squares Support Vector Machine (RBD-LSSVM). In the RBD-LSSVM, multiple LSSVMs are sequentially connected. The second LSSVM uses the fitting residuals of the first LSSVM as input time series, and the third LSSVM trains the residuals of the second, and so on. The original time series is the input of the first LSSVM. Additionally, to obtain the best hyper-parameters for the RBD-LSSVM, we propose a model validation method based on redundancy test using Omni-Directional Correlation Function (ODCF). This method is based on the fact when a model is appropriate for a given time series, there should be no information or correlation in the residuals. We propose the use of ODCF as a statistic to detect nonlinear correlation between two random variables. Thus, we can select hyper-parameters without encountering overfitting, which cannot be avoided by only cross validation using the validation set. We conducted experiments on two time series: annual sunspot number series and monthly Total Column Ozone (TCO) series in New Delhi. Analysis of the prediction results and comparisons with recent and past studies demonstrate the promising performance of the proposed RBD-LSSVM approach with redundancy test based model selection method for modeling and predicting nonlinear time series.