Neural networks for nonlinear regression with serially correlated disturbances: Evidence from cloud cover

2026-06-21

AI Summary

This study addresses the challenge of modeling serially correlated disturbances in nonlinear regression by proposing a novel framework that directly embeds an autoregressive moving average (ARMA) error structure into a feedforward neural network. This approach jointly captures nonlinear functional relationships and error dynamics without relying on lagged variables. The method demonstrates robustness under model misspecification and is validated through extensive simulations and empirical analyses across varying signal-to-noise ratios and sequence lengths. Applied to cloud cover prediction in the Mediterranean region, the proposed model significantly outperforms existing benchmarks—including LSTM—particularly in topographically complex mountainous areas, thereby confirming its superior capability in simultaneously modeling nonlinear effects and temporal dependencies.

Abstract

We propose a new treatment of nonlinear regression with serially correlated disturbances that incorporates autoregressive moving average structures into feedforward neural networks. The resulting model provides an alternative to modeling temporal dependence using lagged variables. In simulations, the proposed method accurately recovers regression functions of varying complexity and the underlying error dynamics across a range of time-series lengths and signal-to-noise ratios. Finite-sample properties and out-of-sample predictive performances are shown to be robust to model misspecification induced by omitted lagged variables and incorrect specification of the error dynamics. Cloud cover is an important factor in climate projections. In an empirical study of cloud cover prediction for a grid of locations within and around the Mediterranean Sea, our proposed model yields more accurate predictions than existing methods, including long short-term memory networks. Improvements are observed broadly and are particularly pronounced in mountain areas relative to linear models with serially correlated errors, consistent with the presence of stronger nonlinear effects in cloud composure in such regions.

Problem

• nonlinear regression
• serially correlated disturbances
• temporal dependence
• cloud cover prediction
• time-series modeling

Innovation

• neural networks
• serially correlated disturbances
• ARMA
• nonlinear regression
• cloud cover prediction