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Port of numpyro_forecast

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# PyMC-Forecast

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Bayesian time-series forecasting with [PyMC](https://www.pymc.io): you write the
generative model; the package handles the train/forecast plumbing, inference,
backtesting, and evaluation.

A PyMC port of [numpyro_forecast](https://github.com/juanitorduz/numpyro_forecast)
(itself a port of Pyro's `pyro.contrib.forecast`) — redesigned around PyMC idioms
rather than a 1:1 translation.

> **Status: early development.** The design and roadmap live in
> [PLAN.md](PLAN.md) and the
> [issue tracker](https://github.com/pymc-labs/pymc-forecast/issues).

**Documentation:** <https://pymc-labs.github.io/pymc-forecast/> — API reference and
executed example notebooks (univariate, hierarchical, covariates, state-space).

## Quickstart

Write a model with one `predict()` call, fit it, and forecast:

```python
import numpy as np, pandas as pd, pymc as pm, pytensor.tensor as pt
from pymc_forecast import Forecaster, backtest, evaluate_forecast, predict, time_series

# a trending weekly series; hold out the last 8 weeks
dates = pd.date_range("2024-01-07", periods=60, freq="W")
y = pd.Series(np.cumsum(np.random.default_rng(0).normal(0.2, 1.0, 60)) + 10, index=dates)
train, test = y.iloc[:52], y.iloc[52:]

def model(h, covariates):
    # a per-step drift latent; time_series adds the matching `_future` latent
    drift = time_series(h, "drift", lambda name, dims: pm.Normal(name, 0.0, 0.5, dims=dims))
    sigma = pm.HalfNormal("sigma", 1.0)
    predict(
        h,
        lambda name, mu, dims, obs: pm.Normal(name, mu, sigma, dims=dims, observed=obs),
        pt.cumsum(drift),                       # local-linear trend
    )

fc = Forecaster(model, train, num_steps=5_000, random_seed=0)   # ADVI
idata = fc.forecast(horizon=8, num_samples=500, random_seed=0)
forecast = idata["predictions"]["forecast"]     # dims: (chain, draw, time_future)
# Outputs stay draw-level (never reduced to means/quantiles); prediction_samples(idata)
# extracts the samples Dataset from a forecast or in-sample result alike.

# score against the held-out weeks (aligned by dim name, not axis position)
truth = test.to_xarray().rename({"index": "time_future"})
print(evaluate_forecast(forecast, truth))       # {'mae': ..., 'rmse': ..., 'crps': ..., 'coverage': ...}

# rolling-origin backtest over the whole series
results = backtest(y, None, model, min_train_window=48, test_window=4, stride=4,
                   num_samples=200, forecaster_options={"num_steps": 3_000}, random_seed=0)
```

Swap `Forecaster` for `HMCForecaster` (NUTS, with `nuts_sampler="nutpie"/"numpyro"/...`)
or `PathfinderForecaster` (pymc-extras) — the fit/forecast interface is identical.
For models with real covariates, pass full-horizon `covariates` to `.forecast()`
instead of `horizon=`, or hand the post-training rows alone to
`future_covariates=` for a forecast conditioned on them. Covariate-free models can also forecast over an exact —
even irregular — later time index with `future_index=`; the horizon length is
derived from it at forecast time. See `markov_time_series` for state-space latents and
`predict_mvn` for observation noise correlated across time.

[pymc-extras statespace](https://github.com/pymc-devs/pymc-extras) structural models
(level/trend, seasonality, SARIMAX, ...) are first-class citizens too: define one as a
`StatespaceModel` and fit it with `StatespaceForecaster` — the same `forecast`
(including exogenous-regression covariates), `predict_in_sample`, `backtest`, and
metrics calls apply, with the Kalman filter marginalizing the latent states instead
of sampling them (see `docs/examples/scan_vs_statespace_local_level.ipynb`).
The pymc-extras integrations (`PathfinderForecaster`, `StatespaceForecaster`) are an
optional extra: install with `pip install 'pymc-forecast[extras]'`.

Priors stay user-injectable on the model object: pass `pymc_extras.prior.Prior`
objects directly to `time_series`/`predict`, or declare named
`default_priors` on a `ForecastingModel`/`StatespaceModel` subclass and let
callers override any subset with `Model(priors={...})` — nested hyper-priors
are shared across the train/forecast split so replay semantics hold.

## Design principles

- **One model trains and forecasts.** In-sample time latents are fitted; the
  forecast horizon uses separate `{name}_future` variables that
  `pm.sample_posterior_predictive` draws from the prior while replaying the
  posterior for everything else.
- **Dims and coords everywhere.** No positional axis conventions: variables carry
  named dims (`"time"`, `"time_future"`, `"obs"`, batch dims), results are
  `arviz.InferenceData` / `xarray` objects with real coordinates, and metrics are
  dim-aware. The [prediction output schema](docs/schema.md) is documented,
  test-locked public API.
- **Not AutoML.** No model zoo, no automatic feature pipelines — a clean path from
  a hand-written PyMC model to probabilistic forecasts and scores.
- **Leverage the ecosystem.** ADVI/NUTS from PyMC core, Pathfinder and state-space
  models from [pymc-extras](https://github.com/pymc-devs/pymc-extras), diagnostics
  and storage from [ArviZ](https://python.arviz.org).

## Development

Requires Python >= 3.11 and [uv](https://docs.astral.sh/uv/):

```bash
uv sync --all-extras
uv run pytest
uv run ruff check .
```

To build the documentation (the example notebooks are committed fully executed;
CI re-executes them with reduced sampling settings):

```bash
uv sync --all-extras --group docs
uv run sphinx-build -b html docs docs/_build/html
```

## License

Apache-2.0. Portions derived from
[numpyro_forecast](https://github.com/juanitorduz/numpyro_forecast) (Apache-2.0).

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