Add extrapolate_season.predict() function

- the function implements a forecasting "method" similar to the
  seasonal naive method
  => instead of simply taking the last observation given a seasonal lag,
     it linearly extrapolates all observations of the same seasonal lag
     from the past into the future; conceptually, it is like the
     seasonal naive method with built-in smoothing
- the function is tested just like the `arima.predict()` and
  `ets.predict()` functions
  + rename the `tests.forecasts.methods.test_ts_methods` module
    into `tests.forecasts.methods.test_predictions`
- re-organize some constants in the `tests` package
- streamline some docstrings

src/urban_meal_delivery/forecasts/methods/__init__.py

@@ -3,3 +3,4 @@
 from urban_meal_delivery.forecasts.methods import arima
 from urban_meal_delivery.forecasts.methods import decomposition
 from urban_meal_delivery.forecasts.methods import ets
+from urban_meal_delivery.forecasts.methods import extrapolate_season

src/urban_meal_delivery/forecasts/methods/extrapolate_season.py

@@ -0,0 +1,72 @@
+"""Forecast by linear extrapolation of a seasonal component."""
+
+import pandas as pd
+from statsmodels.tsa import api as ts_stats
+
+
+def predict(
+    training_ts: pd.Series, forecast_interval: pd.DatetimeIndex, *, frequency: int,
+) -> pd.DataFrame:
+    """Extrapolate a seasonal component with a linear model.
+
+    A naive forecast for each time unit of the day is calculated by linear
+    extrapolation from all observations of the same time of day and on the same
+    day of the week (i.e., same seasonal lag).
+
+    Note: The function does not check if the `forecast_interval`
+    extends the `training_ts`'s interval without a gap!
+
+    Args:
+        training_ts: past observations to be fitted;
+            assumed to be a seasonal component after time series decomposition
+        forecast_interval: interval into which the `training_ts` is forecast;
+            its length becomes the numbers of time steps to be forecast
+        frequency: frequency of the observations in the `training_ts`
+
+    Returns:
+        predictions: point forecasts (i.e., the "prediction" column);
+            includes the four "low/high80/95" columns for the confidence intervals
+            that only contain `NaN` values as this method does not make
+            any statistical assumptions about the time series process
+
+    Raises:
+        ValueError: if `training_ts` contains `NaN` values or some predictions
+            could not be made for time steps in the `forecast_interval`
+    """
+    if training_ts.isnull().any():
+        raise ValueError('`training_ts` must not contain `NaN` values')
+
+    extrapolated_ts = pd.Series(index=forecast_interval, dtype=float)
+    seasonal_lag = frequency * (training_ts.index[1] - training_ts.index[0])
+
+    for lag in range(frequency):
+        # Obtain all `observations` of the same seasonal lag and
+        # fit a straight line through them (= `trend`).
+        observations = training_ts[slice(lag, 999_999_999, frequency)]
+        trend = observations - ts_stats.detrend(observations)
+
+        # Create a point forecast by linear extrapolation
+        # for one or even more time steps ahead.
+        slope = trend[-1] - trend[-2]
+        prediction = trend[-1] + slope
+        idx = observations.index.max() + seasonal_lag
+        while idx <= forecast_interval.max():
+            if idx in forecast_interval:
+                extrapolated_ts.loc[idx] = prediction
+            prediction += slope
+            idx += seasonal_lag
+
+    # Sanity check.
+    if extrapolated_ts.isnull().any():  # pragma: no cover
+        raise ValueError('missing predictions in the `forecast_interval`')
+
+    return pd.DataFrame(
+        data={
+            'prediction': extrapolated_ts.round(5),
+            'low80': float('NaN'),
+            'high80': float('NaN'),
+            'low95': float('NaN'),
+            'high95': float('NaN'),
+        },
+        index=forecast_interval,
+    )