Conformal time series decomposition with component-wise exchangeability

TL;DR

This work presents a novel use of conformal prediction for time series forecasting that incorporates time series decomposition, and finds that the method provides promising results on well-structured time series, but can be limited by factors such as the decomposition step for more complex data.

Abstract

Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to hold for time series due to their temporally correlated nature. In this work, we present a novel use of conformal prediction for time series forecasting that incorporates time series decomposition. This approach allows us to model different temporal components individually. By applying specific conformal algorithms to each component and then merging the obtained prediction intervals, we customize our methods to account for the different exchangeability regimes underlying each component. Our decomposition-based approach is thoroughly discussed and empirically evaluated on synthetic and real-world data. We find that the method provides promising results on well-structured time series, but can be limited by factors such as the decomposition step for more complex data.

Figures (14)

• Figure 1: A high-level overview of our conformal time series decomposition approach. A time series signal is decomposed into individual components, and each component is associated with a specific regime of exchangeability (none, local or global). Relevant conformal methods are applied to each component, producing intermediate prediction intervals which are then recomposed to obtain a prediction interval for the overall time series.
• Figure 2: Illustration of weighting schemes for an exemplary season (grey) with period $\tau=7$. The test sample's location is at the period peak, thus $\tau_{n+1} = 4$.
• Figure 3: Qualitative results for a segment of the synthetic time series for the EnbPI decomposition baseline (left) and our TSD approach with BinaryPoint (right). We observe more efficient PIs across all time steps, but in particular at seasonal peaks and troughs.
• Figure 4: Segments of the three considered real-world time series from multiple domains. From left to right: Different time series complexities are observed as we consider San Diego energy consumption with a shifting trend, Rossman store sales with varying seasonalities, and Beijing air quality exhibiting stronger irregularity and noise. The second row includes prediction intervals leveraging our TSD approaches with the best-performing seasonal weights following \ref{['tab:real_samp']} (left to right: BinaryPoint, ExpLocal, ExpLocal).
• Figure 5: A comparison of decomposition baselines EnbPI and ACI and our weighting mechanisms (\ref{['subsec:season']}) across real-world datasets. Metrics are computed based on obtained intervals for the seasonal component only. The dashed line marks target coverage of $90\%$.

Theorems & Definitions (2)

• definition 1: Exchangeability
• definition 2: Local exchangeability