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Estimating and quantifying uncertainty in system parameters remains a big challenge in applied and computational mathematics. A subset of these problems includes estimating periodic parameters that have unknown dynamics. Along with their time series, the period of these parameters may also be unknown and need to be estimated. The aim of this paper is to address the periodic parameter estimation problem, with particular focus on exploring the associated uncertainty, using Monte Carlo particle methods, such as the ensemble Kalman filter. Both parameter tracking and piecewise function approximations of periodic parameters are considered, highlighting aspects of parameter uncertainty in each approach when considering factors such as the frequency of available data and the number of piecewise segments used in the approximation. Estimation of the period of the periodic parameters and related uncertainty is also analyzed in the piecewise formulation. The pros and cons of each approach are discussed relative to a numerical example estimating the external voltage parameter in the FitzHugh-Nagumo system for modeling the spiking dynamics of neurons.
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This content will become publicly available on July 24, 2026
Simultaneous Detection of Structural Breaks and Outliers in Time Series
This article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive (AR) processes in the presence of outliers. The number and locations of the piecewise AR segments, as well as the orders of the respective AR processes, are assumed to be unknown. In addition, each piece may contain an unknown number of innovational and/or additive outliers. The minimum description length (MDL) principle is applied to compare various segmented AR fits to the data. The goal is to find the “best” combination of the number of segments, the lengths of the segments, the orders of the piecewise AR processes, and the number and type of outliers. Such a “best” combination is implicitly defined as the optimizer of an MDL criterion. Since the optimization is carried over a large number of configurations of segments and positions of outliers, a genetic algorithm is used to find optimal or near‐optimal solutions. Numerical results from simulation experiments and real data analyses show that the procedure enjoys excellent empirical properties.
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- Award ID(s):
- 2210388
- PAR ID:
- 10623840
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Time Series Analysis
- ISSN:
- 0143-9782
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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