Aiming to build foundation models for time-series forecasting and study their scaling behavior, we present here our work-in-progress on Lag-Llama, a general-purpose univariate probabilistic time-series forecasting model trained on a large collection of time-series data. The model shows good zero-shot prediction capabilities on unseen “out-of-distribution” time-series datasets, outperforming supervised baselines. We use smoothly broken power-laws to fit and predict model scaling behavior.