Time Series Modeling of Global Average Absolute Sea Level Change

Abstract

This study aimed to demonstrate the effectiveness of time series models in modeling long-term records of global average absolute sea level changes from 1880 to 2014. Following the Box–Jenkins methodology, the ARIMA(0,1,2) model with drift was identified as the best-fit model for the time series due to its lowest AIC value. Using the LM algorithm, the results revealed that the NARNN model with 7 neurons in the hidden layer and 7 time delays exhibited the best performance among the nonlinear autoregressive neural network models, as indicated by its lower MSE. While ARIMA models excel in modeling linear problems within time series data, NARNN models are better suited for nonlinear patterns. However, a HYBRID model was explored, which combines the strengths of both ARIMA and NARNN models, offering the capability to address both linear and nonlinear aspects of time series data. The comparative analysis of this study demonstrated that the HYBRID model, with 6 neurons in the hidden layer and 7 time delays, outperformed the NARNN model with 7 neurons in the hidden layer and 7 time delays, as well as the ARIMA(0,1,2) model, with the lowest MSE in this study. These findings represent a significant step in time series forecasting by leveraging the strengths of both statistical and machine learning methods.