Model-Based and Model-Free point prediction algorithms for locally stationary random fields
Abstract
The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct one-step-ahead point predictors and compare the performance of Model-free to Model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, Model-free and Model-based, are novel in the context of random fields that are locally (but not globally) stationary. We demonstrate the application of our Model-based and Model-free point prediction methods to synthetic data as well as images from the CIFAR-10 dataset and in the latter case show that our best Model-free point prediction results outperform those obtained using Model-based prediction.
Cite
@article{arxiv.2212.03079,
title = {Model-Based and Model-Free point prediction algorithms for locally stationary random fields},
author = {Srinjoy Das and Yiwen Zhang and Dimitris N. Politis},
journal= {arXiv preprint arXiv:2212.03079},
year = {2022}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1712.02383