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

Abstract

Interval-valued circular observations arise naturally in a wide range of environmental applications, particularly in wind direction monitoring, where directional measurements are observed by an interval of recorded directions over a period. An existing dynamic approach for interval-valued circular time series models the interval boundaries directly on the torus. While such an approach preserves the circular nature of the endpoints, an alternative approach is to consider the centre-range representation of circular intervals. This paper proposes a cylindrical score-driven framework for interval-valued circular time series by representing each interval through a circular centre and a bounded linear width. Dynamic conditional score recursions are developed for the centre and range processes, allowing circular-linear dependence to be captured jointly within a likelihood-based framework. To develop this model, various cylindrical distributions are introduced to accommodate bounded range values. The estimators are investigated through simulations, and the practical usefulness of the framework is illustrated using interval-valued wind direction data from South African and Brazilian wind farms. The proposed methodology provides an alternative approach for modelling the interval-valued circular processes using the directional location and dispersion in interval-valued circular observations.