  Scaling laws for large language models (LLMs) have provided useful guidance
on how to train ever larger models for predictable performance gains. Time
series forecasting shares a similar sequential structure to language, and is
amenable to large-scale transformer architectures. Here we show that
foundational decoder-only time series transformer models exhibit analogous
scaling-behavior to LLMs, while architectural details (aspect ratio and number
of heads) have a minimal effect over broad ranges. We assemble a large corpus
of heterogenous time series data on which to train, and establish, for the
first time, power-law scaling relations with respect to parameter count,
dataset size, and training compute, spanning five orders of magnitude.
