Neural Network-Based Estimation of Time-Dependent Parameters in AR(p) Processes

• URL: http://arxiv.org/abs/2607.00470v1
• Date: Wed, 01 Jul 2026 05:38:14 GMT
• Title: Neural Network-Based Estimation of Time-Dependent Parameters in AR(p) Processes
• Abstract summary: We investigate a forecasting framework based on a simple discrete-time dynamic model with coefficients varying in time.<n>The parameters of the model are recovered within a deep learning framework, which makes it possible to retain a transparent parametric structure.<n>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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• From Atoms to Entropy: Optimal Noise Allocation for Diffusion Training in the Convex Regime [52.459513910242485]
  We develop a general statistical framework for studying optimal noise-level allocation in diffusion training.<n>We show that the optimized training schedule admits an atomic minimizer, concentrated on finitely many noise levels.<n>We then evaluate the entropic schedule in larger-scale experiments, where full schedule optimization is currently intractable.
  arXiv  Detail & Related papers  (2026-07-10T20:59:06Z)
• Factorize to Generalize: Retrieval-Guided Invariant-Dynamic Decomposition for Time Series Forecasting [64.2640656619583]
  Time series foundation models (TSFMs) have recently achieved strong zero-shot forecasting performance through large-scale pretraining and retrieval-augmented prediction.<n>We propose a Retrieval-guided Invariant-Dynamic DEcomposition framework for time series forecasting.
  arXiv  Detail & Related papers  (2026-05-24T07:31:55Z)
• Noise Titration: Exact Distributional Benchmarking for Probabilistic Time Series Forecasting [1.5939955861266883]
  We propose a paradigm shift toward interventionist, exact-statistical benchmarking.<n>We transform forecasting from a black-box sequence matching game into an exact distributional inference task.<n>We find that state-of-the-art zero-shot models behave consistently with the context-parroting mechanism.
  arXiv  Detail & Related papers  (2026-03-23T17:14:11Z)
• Real-Time Learning of Predictive Dynamic Obstacle Models for Robotic Motion Planning [7.819710421921815]
  We develop an online framework to learn, in real-time, a nonlinear predictive model of another agent's motions.<n>A Cadzow projection enforces structured low-rank consistency, yielding a denoised trajectory and local noise variance estimates.<n>We validate the approach in simulation under Gaussian and heavy-tailed noise, and experimentally on a dynamic crane testbed.
  arXiv  Detail & Related papers  (2025-11-02T05:54:30Z)
• Bayesian Models for Joint Selection of Features and Auto-Regressive Lags: Theory and Applications in Environmental and Financial Forecasting [0.9208007322096533]
  We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors.<n>Our framework achieves lower MSPE, improved true model component identification, and greater consistency with autocorrelated noise.<n>Compared to existing methods, our framework achieves lower MSPE, improved true model component identification, and greater consistency with autocorrelated noise.
  arXiv  Detail & Related papers  (2025-08-12T18:44:36Z)
• Spatial Reasoning with Denoising Models [49.83744014336816]
  We introduce a framework to perform reasoning over sets of continuous variables via denoising generative models.<n>For the first time, that order of generation can successfully be predicted by the denoising network itself.<n>Using these findings, we can increase the accuracy of specific reasoning tasks from 1% to >50%.
  arXiv  Detail & Related papers  (2025-02-28T14:08:30Z)
• Neural Superstatistics for Bayesian Estimation of Dynamic Cognitive Models [2.7391842773173334]
  We develop a simulation-based deep learning method for Bayesian inference, which can recover both time-varying and time-invariant parameters. Our results show that the deep learning approach is very efficient in capturing the temporal dynamics of the model.
  arXiv  Detail & Related papers  (2022-11-23T17:42:53Z)
• TACTiS: Transformer-Attentional Copulas for Time Series [76.71406465526454]
  estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. We propose a versatile method that estimates joint distributions using an attention-based decoder. We show that our model produces state-of-the-art predictions on several real-world datasets.
  arXiv  Detail & Related papers  (2022-02-07T21:37:29Z)
• Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics [21.24885597341643]
  Conditional Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and interdimensional correlations. We propose MotionFlow as a novel approach that autoregressively normalizes the output on the temporal input features. We apply our method to different tasks, including prediction, motion prediction time series forecasting, and binary segmentation.
  arXiv  Detail & Related papers  (2021-04-09T14:30:35Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• Causal Modeling with Stochastic Confounders [11.881081802491183]
  This work extends causal inference with confounders. We propose a new approach to variational estimation for causal inference based on a representer theorem with a random input space.
  arXiv  Detail & Related papers  (2020-04-24T00:34:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.