Non-Stationary Spectral Decomposition Network for Econometric Time Series Forecasting

Abstract

Economic and financial time series frequently exhibit persistent trends along with cyclical dynamics whose amplitude, frequency and phase evolve over time due to structural change, policy shocks, and regime transitions. Traditional forecasting models often impose fixed spectral structure or linear dynamics, limiting their ability to represent such nonstationary behavior. This paper introduces the Non-Stationary Spectral Decomposition Network (NS-SDN), a neural state-space architecture designed to model time series as a sum of time-varying sinusoidal components driven by a latent dynamical state. The model learns trend, amplitude, instantaneous frequency, and phase parameters from latent state transitions and synthesizes observations through a spectral emission equation. This formulation combines ideas from implicit neural representations, instantaneous-frequency analysis, and state-space econometric models. Preliminary experiments on financial time series demonstrate stable training and coherent spectral structure, suggesting that state-driven spectral representations may provide a promising framework for forecasting nonstationary economic dynamics.