FedTinyTS: An Ultra-Low-Communication One-Shot Federated Learning Framework for Long-Term Time Series Forecasting

One-shot analytic federated learning in long-term time series forecasting remains challenging due to both high communication costs and limited local adaptation. These methods transmit dense moment matrices whose size grows quadratically with input length, while directly applying the collaboratively estimated knowledge to all clients can underperform local-only training by overlooking client-specific information. We propose FedTinyTS, a one-shot analytic protocol for a channel-independent linear forecasting backbone that removes that quadratic growth, exchanging compact summaries of temporal dependencies in a single round and fitting the model analytically rather than through repeated federated optimization. Because compression can reduce global forecasting performance, FedTinyTS uses reliability-aware aggregation to preserve the quality of the shared model. It further adapts the collaboratively learned knowledge to each client using locally retained information, improving personalized performance without further communication. Across five benchmarks and four horizons, FedTinyTS reduces the message payload by up to $8,548\times$ compared with FedAvg and up to $90.7\times$ compared with dense FedRidge. Averaged across horizons, the global model achieves lower mean squared error than FedAvg on every benchmark but SolarEnergy, and personalization lowers it further on the same four, by up to 3.75%. The dense analytic baselines, which never adapt to a client, instead fall behind a purely local fit by up to 6.31%. Mean absolute error is less favorable, a gap the dense analytic baselines share. Compact temporal summaries therefore retain enough structure to fit a federated forecaster in one round. Code is available at https://anonymous.4open.science/r/FedTinyTS.