  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.
