Guided spiral visualization for periodic time series and residual analysis

Time series in domains such as climate, traffic, and energy often contain multiple, overlapping periodic patterns. Spiral visualizations can support the exploration of such data, but their effectiveness is limited in practice. Outliers and global trends skew the color mapping, dominant periodic components can hide weaker patterns, selecting a meaningful period length is challenging, and comparing subsequences within large datasets remains cumbersome. To address these challenges, we present a guided analytical workflow centered on an enhanced time series spiral visualization. A regression model tailored to periodic data helps identify suitable period lengths and exposes secondary patterns through its residuals. Visual guidance mitigates issues caused by skewed color mappings and highlights relevant spiral sectors even when global trends or outliers are present. Users can interactively select and compare sectors based on measures of average, trend, and similarity, and examine them in linked views or a provenance dashboard, which maintains a record of all user interactions and allows comparing multiple spirals with each other. Application examples demonstrate use cases where the visual sector selection guidance together with the exploration of model residuals leads to insights. In traffic data, for instance, removing the dominant day–night rhythm reveals rush-hour effects that become visible through exploration of the residuals.