Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction
Abstract
Circular data recorded over time, such as wind direction, are increasingly observed in intervals rather than as single point-valued observations, yet no existing framework accommodates data that are simultaneously circular, interval-valued, and temporally dependent. Time series models for point-valued circular data, including recently proposed score-driven approaches, assume that each observation is a single angle. This paper addresses this gap by proposing a dynamic conditional score framework for interval-valued circular time series. The lower and upper boundary sequences of the observed intervals are treated as circular time series governed by score-driven dynamics, which preserves the periodicity of the circular domain and the dependency of boundaries, in which the boundaries are coupled through a toroidal distribution and a jointly derived score. Maximum likelihood estimation is discussed, and their finite-sample performance is evaluated through simulation. An application to interval-valued wind direction data illustrates the practical value of retaining the interval structure within a fully rotationally invariant circular framework.
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BibTeX
@misc{mohan2026intervalvalued,
title = {{Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction}},
author = {Thasmika Mohan and Najmeh Nakhaei Rad and Sphiwe Skhosana and Yaser Samadi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13642},
eprint = {2610.13642},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13642},
}
RIS
TY - UNPB
TI - Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction
AU - Thasmika Mohan
AU - Najmeh Nakhaei Rad
AU - Sphiwe Skhosana
AU - Yaser Samadi
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13642
UR - https://arxiv.org/abs/2610.13642
AB - Circular data recorded over time, such as wind direction, are increasingly observed in intervals rather than as single point-valued observations, yet no existing framework accommodates data that are simultaneously circular, interval-valued, and temporally dependent. Time series models for point-valued circular data, including recently proposed score-driven approaches, assume that each observation is a single angle. This paper addresses this gap by proposing a dynamic conditional score framework for interval-valued circular time series. The lower and upper boundary sequences of the observed intervals are treated as circular time series governed by score-driven dynamics, which preserves the periodicity of the circular domain and the dependency of boundaries, in which the boundaries are coupled through a toroidal distribution and a jointly derived score. Maximum likelihood estimation is discussed, and their finite-sample performance is evaluated through simulation. An application to interval-valued wind direction data illustrates the practical value of retaining the interval structure within a fully rotationally invariant circular framework.
ER -