Optimizing Convergence for Iterative Learning of ARIMA for Stationary Time Series

TL;DR

This paper introduces a new approach combining various Online Gradient Descent algorithms to improve convergence speed and reduce prediction error in ARIMA-based time series forecasting, especially for stationary data.

Contribution

It proposes a novel method that combines different Online Gradient Descent learners for more efficient ARIMA training, addressing computational complexity and convergence issues.

Findings

Outperforms existing methods in prediction accuracy

Achieves faster convergence in training

Reduces computational costs compared to traditional methods

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.