  Transformers have recently gained prominence in long time series forecasting
by elevating accuracies in a variety of use cases. Regrettably, in the race for
better predictive performance the overhead of model architectures has grown
onerous, leading to models with computational demand infeasible for most
practical applications. To bridge the gap between high method complexity and
realistic computational resources, we introduce the Residual Cyclic
Transformer, ReCycle. ReCycle utilizes primary cycle compression to address the
computational complexity of the attention mechanism in long time series. By
learning residuals from refined smoothing average techniques, ReCycle surpasses
state-of-the-art accuracy in a variety of application use cases. The reliable
and explainable fallback behavior ensured by simple, yet robust, smoothing
average techniques additionally lowers the barrier for user acceptance. At the
same time, our approach reduces the run time and energy consumption by more
than an order of magnitude, making both training and inference feasible on
low-performance, low-power and edge computing devices. Code is available at
https://github.com/Helmholtz-AI-Energy/ReCycle
