A Circular Interval-Valued Time Series Model with Application to Wind Direction Prediction

Interval-valued data arise frequently in practice across a wide range of fields, for example, in daily minimum and maximum temperature records and daily opening and closing prices in financial markets. Conventional methods typically aggregate interval observations into single values, such as the mean or midpoint, which may result in a substantial loss of information about the variability and dependency structure. A similar issue arises for circular observations when quantities such as wind direction are recorded as intervals. In Euclidean space, the literature provides only interval-valued autoregressive time series models, whereas on the circle, there remains a clear gap in the modelling of circular interval-valued time series data. The periodic nature of circular data makes standard time series methods inappropriate. To address this gap, this paper introduces an autoregressive time series model for circular interval-valued data. The proposed model accounts for both interval uncertainty and periodic structure. Its performance is evaluated through simulation studies and illustrated using a real dataset, demonstrating its potential as a useful alternative to aggregation-based time series models for the analysis of circular interval data.