Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.13642

Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction

Thasmika Mohan·Najmeh Nakhaei Rad·Sphiwe Skhosana·Yaser Samadi
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

stat.MEstat.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thasmika Mohan, Najmeh Nakhaei Rad, Sphiwe Skhosana, Yaser Samadi. 2026-10-09. Interval-valued circular time series: A toroidal score-driven approach with an application to wind direction. https://arxiv.org/abs/2610.13642

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A Moment-assisted Approach for Improving Subsampling-based MLE with Large-scale data

The maximum likelihood estimation is computationally demanding for large datasets, particularly when the likelihood function includes integrals. Subsampling can reduce the computational burden, but it often results in efficiency loss.This paper proposes a moment-assisted subsampling (MAS) method that can improve the estimation efficiency of existing subsampling-based maximum likelihood estimators.The motivation behind this approach stems from the fact that sample moments can be efficiently computed even if the sample size of the whole data set is huge.Through the generalized method of moments, the proposed method incorporates informative sample moments of the whole data. The MAS estimator can be computed rapidly and is asymptotically normal with a smaller asymptotic variance than the corresponding estimator without incorporating sample moments of the whole data. The asymptotic variance of the proposed estimator depends on the specific sample moments incorporated. We derive the optimal moment that minimizes the resulting asymptotic variance in terms of Loewner order. The proposed MAS estimator can achieve the same estimation efficiency as the whole data-based estimator when the optimal moment is incorporated. Numerical results demonstrate the promising performance of the proposed method in both estimation and computational efficiency compared with existing subsampling methods.

stat.ME↗
arXiv2026

Active Sequential Signal Detection with Asynchronous Decisions

The problem of quickly detecting signals among multiple sequentially observed data streams, subject to constraints on the familywise false-alarm and missed-detection probabilities, is considered under an active sampling setup where only one stream can be sampled at each time instant. Under this setup, it is in general impossible to minimize, even asymptotically, the expected decision time simultaneously for every stream. We therefore consider minimizing the expected time until either the kth signal declaration or termination simultaneously for every k. We first establish non-asymptotic lower bounds for these criteria. For k > |B|, where B denotes the true subset of signals, we show that these lower bounds are attained asymptotically as the error levels vanish by any policy that stops sampling and makes a decision for each stream according to a local Sequential Probability Ratio Test. For 1 <= k <= |B|, however, the performance depends critically on the sampling rule, and we propose one with a simple exploration mechanism that prevents switching away from signals prematurely because of early unfavorable observations. We show that, under a mild relative-rate condition on the two error levels, the resulting policy attains all the lower bounds simultaneously. Numerical studies are presented to compare the proposed policy with an oracle policy and a follow-the-leader policy.

stat.ME↗
arXiv2026

Typical Healthcare Pathways as a Basis for Admixture Modeling of Patient Trajectories

Background: Understanding whether patients follow similar or distinct patterns of care is important for characterizing clinical practice, identifying patient subgroups, and supporting quality improvement. However, routine healthcare trajectories are difficult to compare directly because patients may differ in their diagnostic workup, treatment sequencing, timing of clinical events, and documentation practices. Despite this variation, trajectories often contain recurring patterns at the cohort level. Methods: To address this challenge, we present a framework that explicitly separates cohort-level typical pathway identification from patient-level inference. At the cohort level, we derive an interpretable representation of care processes using a rule-based algorithm to identify typical healthcare pathways, resulting in a compact pathway graph. These pathways are then modeled as Markov chains and used as structured components in an admixture model, allowing each patient to be represented as a probabilistic mixture of typical pathways rather than being assigned to a single pathway component. The resulting admixture weights provide a compact representation of patient trajectories for subgroup characterization. We further assess the stability of the identified pathways and inferred admixture representations across multiple train-test splits. Results: Across train-test splits, the framework demonstrated consistent pathway structures and patient-level mixture patterns. Applied to routine care data from prostate cancer patients undergoing radical prostatectomy, the framework identified interpretable care patterns and supported the identification of patient subgroups with similar clinical event patterns. Conclusion: Overall, the proposed framework provides an interpretable and stable approach for summarizing treatment pathways and characterizing patient subgroups in real-world practice.

stat.ME↗