Comprehensive Learning Polynomial Auto-Regressive Model based on Optimization with Application of Time Series Forecasting

Nowadays, time series analysis is an important challenge in engineering problems. This paper proposes a Comprehensive Learning Polynomial Autoregressive Model for predicting linear and nonlinear time series. The model is based on the autoregressive model but developed in a polynomial aspect to make it more robust and accurate. The model predicts future values by learning the weights of the weighted sum of the polynomial combination of previous data. The learning process for the hyperparameters and properties of the model in the training phase is performed by the metaheuristic optimization method. Using this model, we can predict nonlinear time series, as well as linear time series. The proposed method was implemented on eight standard stationary and non-stationary large-scale real-world datasets. It outperformed the state-of-the-art methods that use deep learning in seven time series and has better results compared to all other methods in six datasets. Experimental results show the advantage of the model’s accuracy over other compared methods on various prediction tasks based on the root-mean-square error.