A1907
Title: Prediction inference of time series with standard ReLU deep neural networks
Authors: Kejin Wu - Loyola University Chicago (United States) [presenting]
Abstract: A methodology based on standard ReLU Deep Neural Networks (DNN) is proposed to make prediction inference with uncertainty quantification. Classically, linear, nonlinear, or nonparametric kernel methods have been relied upon to fit and predict time series. As the universal approximation ability of DNN was revealed, the application of DNN has become increasingly popular for prediction tasks in various scientific areas. However, the corresponding uncertainty quantification has not been studied thoroughly. Particularly, the uncertainty in prediction consists of two parts: (1) future variability and (2) estimation variability within training data. To capture both variabilities, a pertinent prediction interval (PPI) is built with the DNN model estimator. First, the consistency property of the DNN estimator with Beta-mixing dependent data is explored. Subsequently, it is shown that the implied forward bootstrap series is still Beta-mixing and possesses the same stationary distribution as the original time series in probability, which is a key condition for enabling the PPI. Finally, the desired PPI is constructed after imposing minimal conditions on the limiting distribution of predictive roots. Simulations and real-data analysis are deployed to evaluate the method against standard nonparametric and purely Deep-learning methods.
