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

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. Serially correlated disturbances in place of lagged variables improve predictive accuracy across a range of land and ocean environments. Improvements over linear models with serially correlated disturbances are particularly pronounced in mountain areas, consistent with the presence of stronger nonlinear effects in cloud formation in such regions.