Neural Network-Based Estimation of Time-Dependent Parameters in AR(p) Processes
This work offers a hybrid approach combining parametric interpretability with deep learning flexibility for nonstationary time series forecasting, but it is incremental as it applies existing ideas to a specific model class.
The paper proposes a neural network-based method to estimate time-varying parameters in autoregressive (AR(p)) processes, enabling forecasting under Gaussian and Laplace noise. Numerical experiments on TVAR(1) show the model produces valid prediction intervals and competitive forecasts.
We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time. The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure while simultaneously accounting for complex and nonstationary patterns in the observed phenomenon. Our analysis covers two specifications of the noise process. Besides the standard Gaussian setting, we also consider Laplace-distributed noise, which can offer a more adequate description in the presence of heavier tails and sharper local fluctuations. For both cases, we formulate the predictive scheme of the model and analyze the associated uncertainty quantification, including the construction of prediction intervals. The results illustrate that a relatively simple model, when combined with time-dependent parameter estimation, can serve as a mathematically tractable and practically flexible tool for forecasting complex dynamics under different noise assumptions. The general model is stated for TVAR($p$), while the prediction-interval formulas and the numerical experiments are developed for the TVAR(1) case.