A novel approach to forecast time series exhibiting aperiodic cycles using Exponential Autoregressive Moving Average models

When modeling real-world processes, the data generating process may exhibit behavior such as significant aperiodic cycles with variable peaks and troughs. In such cases, which can be ascertained through periodogram analysis, non-linear time-series models are crucial. Evolved from the family of Exponential Autoregressive (EXPAR) models which are well recognized for capturing the random cyclic vibrations, the Exponential Autoregressive Moving Average (EXPARMA) models has been proposed. The problem although applying such models is that no simple approach is available in the literature for fitting such models to real datasets. This work proposes a straightforward, yet effective method for estimating the model parameters and making out-of-sample predictions. The proposed methodology incorporated simple concepts such as minimization of residual sum of squares and choosing the appropriate model order by utilizing information criterion. The effectiveness of the developed algorithm has been highlighted through an application. Forecasts obtained by implementing the developed algorithm have been compared in terms of error. The considered error metrics clearly highlight the superiority of the developed methodology, providing up to about 40% increase in accuracy. Overall, the results suggest that the discussed model can be used to capture the cyclical nature of the data generated in real-world scenarios.