  By encoding time series as a string of numerical digits, we can frame time
series forecasting as next-token prediction in text. Developing this approach,
we find that large language models (LLMs) such as GPT-3 and LLaMA-2 can
surprisingly zero-shot extrapolate time series at a level comparable to or
exceeding the performance of purpose-built time series models trained on the
downstream tasks. To facilitate this performance, we propose procedures for
effectively tokenizing time series data and converting discrete distributions
over tokens into highly flexible densities over continuous values. We argue the
success of LLMs for time series stems from their ability to naturally represent
multimodal distributions, in conjunction with biases for simplicity, and
repetition, which align with the salient features in many time series, such as
repeated seasonal trends. We also show how LLMs can naturally handle missing
data without imputation through non-numerical text, accommodate textual side
information, and answer questions to help explain predictions. While we find
that increasing model size generally improves performance on time series, we
show GPT-4 can perform worse than GPT-3 because of how it tokenizes numbers,
and poor uncertainty calibration, which is likely the result of alignment
interventions such as RLHF.
