Add urban_meal_delivery.forecasts.models sub-package

- `*Model`s use the `methods.*.predict()` functions to predict demand
  given an order time series generated by `timify.OrderHistory`
- `models.base.ForecastingModelABC` unifies how all `*Model`s work
  and implements a caching strategy
- implement three `*Model`s for tactical forecasting, based on the
  hets, varima, and rtarima models described in the first research paper
- add overall documentation for `urban_meal_delivery.forecasts` package
- move the fixtures in `tests.forecasts.timify.conftest` to
  `tests.forecasts.conftest` and adjust the horizon of the test horizon
  from two to three weeks

src/urban_meal_delivery/forecasts/models/tactical/vertical.py

@@ -0,0 +1,119 @@
+"""Vertical forecasting `*Model`s to predict demand for tactical purposes.
+
+Vertical `*Model`s take order counts of all time steps in the training data
+and make a prediction for all time steps on the day to be predicted at once.
+Thus, the training time series have a `frequency` of the number of weekdays,
+`7`, times the number of time steps on a day. For example, with 60-minute time
+steps, the `frequency` becomes `7 * 12` (= operating hours from 11 am to 11 pm),
+which is `84`. Vertical `*Model`s train the forecasting `methods` on a seasonally
+decomposed time series internally.
+"""  # noqa:RST215
+
+import datetime as dt
+
+import pandas as pd
+
+from urban_meal_delivery import db
+from urban_meal_delivery.forecasts import methods
+from urban_meal_delivery.forecasts.models import base
+
+
+class VerticalARIMAModel(base.ForecastingModelABC):
+    """The ARIMA model applied on a vertical time series."""
+
+    name = 'varima'
+
+    def predict(
+        self, pixel: db.Pixel, predict_at: dt.datetime, train_horizon: int,
+    ) -> pd.DataFrame:
+        """Predict demand for a time step.
+
+        Args:
+            pixel: pixel in which the prediction is made
+            predict_at: time step (i.e., "start_at") to make the prediction for
+            train_horizon: weeks of historic data used to predict `predict_at`
+
+        Returns:
+            actual order counts (i.e., the "actual" column),
+                point forecasts (i.e., the "prediction" column), and
+                confidence intervals (i.e, the four "low/high/80/95" columns);
+                contains several rows, including one for the `predict_at` time step
+
+        # noqa:DAR401 RuntimeError
+        """
+        # Generate the historic (and vertical) order time series.
+        training_ts, frequency, actuals_ts = self._order_history.make_vertical_ts(
+            pixel_id=pixel.id,
+            predict_day=predict_at.date(),
+            train_horizon=train_horizon,
+        )
+
+        # Decompose the `training_ts` to make predictions for the seasonal
+        # component and the seasonally adjusted observations separately.
+        decomposed_training_ts = methods.decomposition.stl(
+            time_series=training_ts,
+            frequency=frequency,
+            # "Periodic" `ns` parameter => same seasonal component value
+            # for observations of the same lag.
+            ns=999,
+        )
+
+        # Make predictions for the seasonal component by linear extrapolation.
+        seasonal_predictions = methods.extrapolate_season.predict(
+            training_ts=decomposed_training_ts['seasonal'],
+            forecast_interval=actuals_ts.index,
+            frequency=frequency,
+        )
+
+        # Make predictions with the ARIMA model on the seasonally adjusted time series.
+        seasonally_adjusted_predictions = methods.arima.predict(
+            training_ts=(
+                decomposed_training_ts['trend'] + decomposed_training_ts['residual']
+            ),
+            forecast_interval=actuals_ts.index,
+            # Because the seasonality was taken out before,
+            # the `training_ts` has, by definition, a `frequency` of `1`.
+            frequency=1,
+            seasonal_fit=False,
+        )
+
+        # The overall `predictions` are the sum of the separate predictions above.
+        # As the linear extrapolation of the seasonal component has no
+        # confidence interval, we put the one from the ARIMA model around
+        # the extrapolated seasonal component.
+        predictions = pd.DataFrame(
+            data={
+                'actual': actuals_ts,
+                'prediction': (
+                    seasonal_predictions['prediction']  # noqa:WPS204
+                    + seasonally_adjusted_predictions['prediction']
+                ),
+                'low80': (
+                    seasonal_predictions['prediction']
+                    + seasonally_adjusted_predictions['low80']
+                ),
+                'high80': (
+                    seasonal_predictions['prediction']
+                    + seasonally_adjusted_predictions['high80']
+                ),
+                'low95': (
+                    seasonal_predictions['prediction']
+                    + seasonally_adjusted_predictions['low95']
+                ),
+                'high95': (
+                    seasonal_predictions['prediction']
+                    + seasonally_adjusted_predictions['high95']
+                ),
+            },
+            index=actuals_ts.index,
+        )
+
+        # Sanity checks.
+        if len(predictions) <= 1:  # pragma: no cover
+            raise RuntimeError('vertical models should predict several time steps')
+        if predictions.isnull().any().any():  # pragma: no cover
+            raise RuntimeError('missing predictions in varima model')
+        if predict_at not in predictions.index:  # pragma: no cover
+            raise RuntimeError('missing prediction for `predict_at`')
+
+        return predictions