intervalsseasonal

Intervalsseasonal is a term used to describe a framework in time series analysis that treats seasonality through interval-valued representations rather than single-point estimates. In this approach, each seasonal effect is represented as an interval [L, U], capturing a range of plausible values within the cycle and explicitly accounting for uncertainty and within-season variability.

Construction typically starts with selecting a seasonal cycle (calendar-based, trading days, or a custom period). The data are partitioned into seasons, and for each position in the cycle an interval estimate of the seasonal effect is derived using methods such as bootstrapping, robust statistics, or probabilistic models. The result is a seasonal component expressed as a sequence of intervals across the cycle, rather than fixed numbers.

Modeling and forecasting with intervalsseasonal often pair interval-based decomposition with trend and irregular components. Forecasts yield interval predictions for each season, providing prediction intervals that reflect both overall uncertainty and seasonal variability. Techniques used include interval regression for seasonal effects, interval ARIMA variants, and Bayesian interval models that produce full predictive intervals.

Applications span domains with strong or variable seasonality, such as energy demand, climate and meteorology, retail sales, and transport. Benefits of this approach include explicit quantification of seasonal uncertainty and robustness to outliers. Limitations can include higher computational demands, increased model complexity, and interpretability challenges, especially when communicating interval-valued outputs to non-technical stakeholders.

Overall, intervalsseasonal offers a principled way to model and forecast seasonal phenomena while preserving uncertainty within seasonal patterns. See also interval arithmetic, interval-valued time series, seasonal decomposition, and probabilistic forecasting.