A1444
Title: On the theoretical foundations of neural network-based time series: Stationarity, ergodicity, and generalization
Authors: Dongwon Kim - Korea Institute for Advanced Study (KIAS) (Korea, South) [presenting]
Abstract: Stationarity and ergodicity play a central role in time series analysis, forming the theoretical basis for consistent estimation, asymptotic normality, and the validity of statistical inference. While these properties have been well studied in classical models such as ARMA and GARCH, their theoretical understanding in neural network-based time series models remains limited. Sufficient conditions for the stationarity and ergodicity of multivariate neural network autoregressive moving average (NN-ARMA) processes are developed. The analysis builds upon the iterated random function (IRF) approach, providing a general theoretical foundation for the stability of nonlinear stochastic systems driven by neural architectures. Furthermore, the generalization capability of stationary ergodic NN-ARMA models through Rademacher complexity bounds is investigated. By adapting results, generalization error bounds under weak dependence are derived, bridging statistical learning theory and time-series ergodic theory. Together, these results aim to establish a unified framework that links the theoretical stability of neural network time series models with their learning capacity, offering insights into both the probabilistic and algorithmic behavior of modern stochastic neural models.
