Adaptive deep learning for nonlinear time series models

arXiv:2207.02546v3 Announce Type: replace-cross
Abstract: In this paper, we develop a general theory for adaptive nonparametric estimation of the mean function of a non-stationary and nonlinear time series model using deep neural networks (DNNs). We first consider two types of DNN estimators, non-penalized and sparse-penalized DNN estimators, and establish their generalization error bounds for general non-stationary time series. We then derive minimax lower bounds for estimating mean functions belonging to a wide class of nonlinear autoregressive (AR) models that include …

abstract arxiv deep learning dnn error function general math.st mean networks neural networks paper series stat.ml stat.th theory time series type types