Optimizing Convergence for Iterative Learning of ARIMA for Stationary Time Series

Abstract: Forecasting of time series in continuous systems becomes an increasingly relevant task due to recent developments in IoT and 5G. The popular forecasting model ARIMA is applied to a large variety of applications for decades. An online variant of ARIMA applies the Online Newton Step in order to learn the underlying process of the time series. This optimization method has pitfalls concerning the computational complexity and convergence. Thus, this work focuses on the computational less expensive Online Gradient Descent optimization method, which became popular for learning of neural networks in recent years. For the iterative training of such models, we propose a new approach combining different Online Gradient Descent learners (such as Adam, AMSGrad, Adagrad, Nesterov) to achieve fast convergence. The evaluation on synthetic data and experimental datasets show that the proposed approach outperforms the existing methods resulting in an overall lower prediction error.