2022/10/20 by Mingliang Ma, Ma, Mingliang, Abolfazl Safikhani +1
Computer Science · Decision Sciences · Engineering · #Energy Load and Power Forecasting #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Stock Market Forecasting Methods
paper · pdf · doi:10.48550/arxiv.2210.11530
openalex publication_date 2022/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Deep neural networks are powerful tools to model observations over time with non-linear patterns. Despite the widespread use of neural networks in such settings, most theoretical developments of deep neural networks are under the assumption of independent observations, and theoretical results for temporally dependent observations are scarce. To bridge this gap, we study theoretical properties of deep neural networks on modeling non-linear time series data. Specifically, non-asymptotic bounds for prediction error of (sparse) feed-forward neural network with ReLU activation function is established under mixing-type assumptions. These assumptions are mild such that they include a wide range of time series models including auto-regressive models. Compared to independent observations, established convergence rates have additional logarithmic factors to compensate for additional complexity due to dependence among data points. The theoretical results are supported via various numerical simulation settings as well as an application to a macroeconomic data set.