Detection of Structural Distortions in Functional Time Series

2026-08-13

AI Summary

This study addresses the challenges of detecting local structural distortions and low signal-to-noise ratios in functional time series by proposing a novel detection method based on Bayesian state-space models. By constructing a Bayesian framework to capture local heterogeneous distortions and designing an efficient blocked Gibbs sampling algorithm to aggregate multidimensional information, the approach achieves precise identification of local change points in functional data. Empirical evaluations on financial and temperature datasets demonstrate that the proposed method effectively mitigates noise interference while significantly enhancing detection accuracy and robustness. Consequently, this work provides a reliable theoretical tool and practical solution for the structural analysis of complex functional data.

Abstract

In the era of modern data science, the rapid proliferation of high-dimensional and functional datasets has fostered increasing interest in the investigation of paradigm shifts and structural breaks. Unlike classical univariate time series, structural changes in functional data need not occur simultaneously across the entire domain; instead, they may emerge locally, producing heterogeneous distortions across the underlying functional structure. The patterns of instability often exhibit sparsity, where it is not known \textit{a priori} which specific parameters are undergoing a transition. However, in functional contexts, these shifts are often "localised". The difficulty lies in the high dimensionality of the parameter space, where the signal-to-noise ratio may be low for individual components, necessitating the aggregation of information across dimensions to detect a global change. This paper addresses the problem of detecting structural shifts in a functional time series from a Bayesian perspective. We have developed various novel methodologies that capture the inherent structural distortion in a sequence of random functions, both individually and simultaneously. The formulation of the problem is based on the state-space representation of a functional time series. Efficient Blocked Gibbs Sampling algorithms have been proposed to identify these locations accurately. Further, we demonstrate the effectiveness of our methods on several financial and temperature datasets.

Problem

• Functional Time Series
• Structural Distortions
• Change Point Detection
• High-dimensional Data
• Localised Shifts

Innovation

• Functional Time Series
• Bayesian Structural Change Detection
• State-Space Model
• Blocked Gibbs Sampling
• Localised Distortions