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This paper considers improved forecasting in possibly nonlinear dynamicsettings, with high-dimension predictors ("big data" environments). To overcomethe curse of dimensionality and manage data and model complexity, we examineshrinkage estimation of a back-propagation algorithm of a deep neural net withskip-layer connections. We expressly include both linear and nonlinearcomponents. This is a high-dimensional learning approach including bothsparsity L1 and smoothness L2 penalties, allowing high-dimensionality andnonlinearity to be accommodated in one step. This approach selects significantpredictors as well as the topology of the neural network. We estimate optimalvalues of shrinkage hyperparameters by incorporating a gradient-basedoptimization technique resulting in robust predictions with improvedreproducibility. The latter has been an issue in some approaches. This isstatistically interpretable and unravels some network structure, commonly leftto a black box. An additional advantage is that the nonlinear part tends to getpruned if the underlying process is linear. In an application to forecastingequity returns, the proposed approach captures nonlinear dynamics betweenequities to enhance forecast performance. It offers an appreciable improvementover current univariate and multivariate models by RMSE and actual portfolioperformance.

Forecasting in Big Data Environments: an Adaptable and Automated Shrinkage Estimation of Neural Networks (AAShNet)