[Paper Review] Retrieval Based Time Series Forecasting

Baoyu Jing, Si Zhang+5 more|arXiv (Cornell University)|Sep 27, 2022

Time Series Analysis and Forecasting4 citations

TL;DR

This paper proposes ReTime, a retrieval-based time series forecasting method that improves accuracy under high missing rates by leveraging relational retrieval of relevant historical time series as references. Theoretical analysis shows that references reduce prediction uncertainty, and empirical results demonstrate ReTime's superior performance on real-world datasets, especially when forecasting horizons are long.

ABSTRACT

Time series data appears in a variety of applications such as smart transportation and environmental monitoring. One of the fundamental problems for time series analysis is time series forecasting. Despite the success of recent deep time series forecasting methods, they require sufficient observation of historical values to make accurate forecasting. In other words, the ratio of the output length (or forecasting horizon) to the sum of the input and output lengths should be low enough (e.g., 0.3). As the ratio increases (e.g., to 0.8), the uncertainty for the forecasting accuracy increases significantly. In this paper, we show both theoretically and empirically that the uncertainty could be effectively reduced by retrieving relevant time series as references. In the theoretical analysis, we first quantify the uncertainty and show its connections to the Mean Squared Error (MSE). Then we prove that models with references are easier to learn than models without references since the retrieved references could reduce the uncertainty. To empirically demonstrate the effectiveness of the retrieval based time series forecasting models, we introduce a simple yet effective two-stage method, called ReTime consisting of a relational retrieval and a content synthesis. We also show that ReTime can be easily adapted to the spatial-temporal time series and time series imputation settings. Finally, we evaluate ReTime on real-world datasets to demonstrate its effectiveness.

Motivation & Objective

• Address the challenge of high uncertainty in time series forecasting when historical observations are limited, especially under high missing rates (e.g., 0.8).
• Theoretically quantify prediction uncertainty using conditional entropy and link it to Mean Squared Error (MSE).
• Demonstrate that models using retrieved references are easier to train due to reduced uncertainty.
• Develop a practical two-stage method, ReTime, for effective time series forecasting, imputation, and spatial-temporal modeling.
• Empirically validate ReTime’s effectiveness across multiple real-world datasets and settings.

Proposed method

• ReTime employs a two-stage framework: first, relational retrieval identifies relevant reference time series based on structural or topological relationships (e.g., sensor adjacency), not content similarity.
• Relational retrieval ensures reliability even when input historical values are sparse or corrupted.
• Second, content synthesis combines the target time series and retrieved references to generate future values using a learnable synthesis module.
• The method is adaptable to spatial-temporal forecasting and time series imputation by treating the target’s own historical snippet as the top reference.
• Theoretical analysis proves that reference-based models reduce uncertainty by lowering the conditional entropy of predictions.
• The framework is evaluated with ablation studies on hyperparameters, including the number of references K, showing optimal performance at K=5–10.

Experimental results

Research questions

• RQ1 Can the uncertainty in time series forecasting be theoretically quantified and linked to standard metrics like MSE?
• RQ2 Does retrieving relevant reference time series reduce prediction uncertainty and improve model generalization, especially under high missing rates?
• RQ3 Can a two-stage method combining relational retrieval and content synthesis outperform existing deep learning models in long-horizon forecasting?
• RQ4 Is the proposed ReTime framework effective not only for forecasting but also for time series imputation and spatial-temporal modeling?
• RQ5 How does the number of retrieved references (K) affect the performance and computational cost of ReTime?

Key findings

• Theoretical analysis confirms that prediction uncertainty, measured via conditional entropy, is directly related to Mean Squared Error (MSE), providing a formal basis for uncertainty quantification.
• Models using retrieved references exhibit lower uncertainty and are easier to train, as references reduce the effective complexity of the prediction task.
• ReTime achieves state-of-the-art performance on real-world datasets, particularly excelling under high missing rates (e.g., 0.8), where standard models degrade significantly.
• The optimal number of references (K) for ReTime lies between 5 and 10, balancing performance and computational cost.
• Training time and GPU memory usage grow linearly with K, indicating predictable and scalable resource usage.