  In recent years, both online and offline deep learning models have been
developed for time series forecasting. However, offline deep forecasting models
fail to adapt effectively to changes in time-series data, while online deep
forecasting models are often expensive and have complex training procedures. In
this paper, we reframe the online nonlinear time-series forecasting problem as
one of linear hyperdimensional time-series forecasting. Nonlinear
low-dimensional time-series data is mapped to high-dimensional
(hyperdimensional) spaces for linear hyperdimensional prediction, allowing
fast, efficient and lightweight online time-series forecasting. Our framework,
TSF-HD, adapts to time-series distribution shifts using a novel co-training
framework for its hyperdimensional mapping and its linear hyperdimensional
predictor. TSF-HD is shown to outperform the state of the art, while having
reduced inference latency, for both short-term and long-term time series
forecasting. Our code is publicly available at
http://github.com/tsfhd2024/tsf-hd.git
