PRISM: A hierarchical multiscale approach for time series forecasting

TL;DR

PRISM addresses the challenge of forecasting multiscale time series by learning a unified time–frequency hierarchy built as a binary, overlapping time tree with per-node Haar wavelet (or alternative) bands. At each node, frequency bands are weighted by learnable importance scores and recombined to form a reconstructible multiscale representation that feeds task-specific forecasters, enabling accurate, interpretable forecasts. Across diverse benchmarks, PRISM achieves state-of-the-art performance and demonstrates robustness to irregularity, incompleteness, nonstationarity, and drift, while maintaining efficiency and interpretability. The approach opens avenues for extensions to adaptive frequency bases, irregular temporal partitions, and multivariate forecasting, highlighting the value of explicit time–frequency hierarchies in real-world forecasting tasks.

Abstract

Forecasting is critical in areas such as finance, biology, and healthcare. Despite the progress in the field, making accurate forecasts remains challenging because real-world time series contain both global trends, local fine-grained structure, and features on multiple scales in between. Here, we present a new forecasting method, PRISM (Partitioned Representation for Iterative Sequence Modeling), that addresses this challenge through a learnable tree-based partitioning of the signal. At the root of the tree, a global representation captures coarse trends in the signal, while recursive splits reveal increasingly localized views of the signal. At each level of the tree, data are projected onto a time-frequency basis (e.g., wavelets or exponential moving averages) to extract scale-specific features, which are then aggregated across the hierarchy. This design allows the model to jointly capture global structure and local dynamics of the signal, enabling accurate forecasting. Experiments across benchmark datasets show that our method outperforms state-of-the-art methods for forecasting. Overall, these results demonstrate that our hierarchical approach provides a lightweight and flexible framework for forecasting multivariate time series. The code is available at https://github.com/nerdslab/prism.

Figures (5)

• Figure 1: The PRISM model overview. The time series is partitioned into chunks recrusively to produce smaller temporal segments. At each level of this splitting procedure, we apply learnable filter banks that use time-frequency representations and learnable weights to extract features from the segment. The weights at each level of the feature hierarchy are distinct and not shared, allowing the model to extract different sets of coefficients that are meaningful for forecasting. The learning is driven by the forecasting loss on predictions of the future of the time series.
• Figure 2: Forecasting performance across GIFT dataset property groups. Columns show the overall counts on best forecasting performance (lowest MSE / MAE) across all datasets and counts within groups defined by dataset-level properties. A single dataset may contribute to multiple columns.
• Figure 3: Multiscale features learned by the model and their impact on time series prediction tasks. (Top) multiscale signal components from different time- and frequency levels (L and R stands for left and right tree nodes in time decomposition; $w$ is the associated importance weight), (middle) cumulative forecast of the time series based on these components, (bottom) cumulative reconstruction of the time series from these components.
• Figure 4: Importance scores across ETT datasets. The scores for the ETTm1 dataset at forecast length of 720 (blue) compared across different (A) seeds, (B) segments of the time series, (C) forecast lengths, (D) datasets, (E) numbers of Wavelet bands, and (F) sampling rates.
• Figure 5: PRISM interpretation scheme. (Left) The Wavelet transformation decomposes time series into components localized in frequency and time. The time series forecast then can be done using feedforward MLP networks applied to each Wavelet component. The required number of MLPs grows exponentially with the number of Wavelet levels. (Right) PRISM effectively reduces the number of required MLPs by selecting only the Wavelet components relevant for forecasting and combining them to the extents necessary for forecasting.