  It is challenging to scale time series forecasting models such that they
forecast accurately for multiple distinct domains and datasets, all with
potentially different underlying collection procedures (e.g., sample
resolution), patterns (e.g., periodicity), and prediction requirements (e.g.,
reconstruction vs. forecasting). We call this general task universal
forecasting. Existing methods usually assume that input data is regularly
sampled, and they forecast to pre-determined horizons, resulting in failure to
generalise outside of the scope of their training. We propose the DAM - a
neural model that takes randomly sampled histories and outputs an adjustable
basis composition as a continuous function of time for forecasting to non-fixed
horizons. It involves three key components: (1) a flexible approach for using
randomly sampled histories from a long-tail distribution, that enables an
efficient global perspective of the underlying temporal dynamics while
retaining focus on the recent history; (2) a transformer backbone that is
trained on these actively sampled histories to produce, as representational
output, (3) the basis coefficients of a continuous function of time. We show
that a single univariate DAM, trained on 25 time series datasets, either
outperformed or closely matched existing SoTA models at multivariate long-term
forecasting across 18 datasets, including 8 held-out for zero-shot transfer,
even though these models were trained to specialise for each dataset-horizon
combination. This single DAM excels at zero-shot transfer and very-long-term
forecasting, performs well at imputation, is interpretable via basis function
composition and attention, can be tuned for different inference-cost
requirements, is robust to missing and irregularly sampled data {by design}.
