Neural Network-Based Estimation of Time-Dependent Parameters in AR(p) Processes
2026-07-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a simple time-based model that changes its settings as time goes on to predict future data. They use deep learning to find these changing settings, allowing the model to stay easy to understand while still handling complicated patterns. They look at two different types of random noise in the data: one that is common (Gaussian) and another that better captures sudden big changes (Laplace). The authors create a method to make predictions and measure how uncertain these predictions are, including making prediction ranges. Their work shows that even a straightforward model can effectively forecast complex changes when its parameters are allowed to vary over time.
time-varying autoregressive modeldeep learningnonstationary time seriesGaussian noiseLaplace noiseprediction intervalsuncertainty quantificationdynamic modelingforecastingparametric modeling
Authors
Agnieszka Kopeć, Paweł Przybyłowicz, Martyna Wiącek
Abstract
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.