[ENH] Rework ETS Forecaster (#2939)

* iterative

* iterative ETS

* notebook

* Fix bug in seasonality calculation

* Add example for ETS iterative forecasting

* ets tests

* holding notebook

* example

* Run Itertive notebook

---------

Co-authored-by: Alex Banwell <arb1g19@soton.ac.uk>

Author: TonyBagnall

aeon/forecasting/_ets.py

@@ -1,7 +1,8 @@
 """ETSForecaster class.
 
 An implementation of the exponential smoothing statistics forecasting algorithm.
-Implements additive and multiplicative error models.
+Implements additive and multiplicative error models. We recommend using the AutoETS
+version, but this is useful for demonstrations.
 """
 
 __maintainer__ = []
@@ -85,7 +86,7 @@ class ETSForecaster(BaseForecaster):
     ...     seasonality_type='multiplicative', seasonal_period=4
     ... )
     >>> forecaster.forecast(y)
-    366.90200486015596
+    365.5141941111267
     """
 
     _tags = {
@@ -193,7 +194,7 @@ def _get_int(x):
             self._gamma,
             self.phi,
         )
-        self.forecast_ = _predict(
+        self.forecast_ = _numba_predict(
             self._trend_type,
             self._seasonality_type,
             self.level_,
@@ -240,6 +241,29 @@ def _initialise(self, data):
             self._trend_type, self._seasonality_type, self._seasonal_period, data
         )
 
+    def iterative_forecast(self, y, prediction_horizon):
+        """Forecast with ETS specific iterative method.
+
+        Overrides the base class iterative_forecast to avoid refitting on each step.
+        This simply rolls the ETS model forward
+        """
+        self.fit(y)
+        preds = np.zeros(prediction_horizon)
+        preds[0] = self.forecast_
+        for i in range(1, prediction_horizon):
+            preds[i] = _numba_predict(
+                self._trend_type,
+                self._seasonality_type,
+                self.level_,
+                self.trend_,
+                self.seasonality_,
+                self.phi,
+                i + 1,
+                self.n_timepoints_,
+                self._seasonal_period,
+            )
+        return preds
+
 
 @njit(fastmath=True, cache=True)
 def _numba_fit(
@@ -268,20 +292,18 @@ def _numba_fit(
         time_point = data[index]
 
         # Calculate level, trend, and seasonal components
-        fitted_value, error, level, trend, seasonality[t % seasonal_period] = (
-            _update_states(
-                error_type,
-                trend_type,
-                seasonality_type,
-                level,
-                trend,
-                seasonality[s_index],
-                time_point,
-                alpha,
-                beta,
-                gamma,
-                phi,
-            )
+        fitted_value, error, level, trend, seasonality[s_index] = _update_states(
+            error_type,
+            trend_type,
+            seasonality_type,
+            level,
+            trend,
+            seasonality[s_index],
+            time_point,
+            alpha,
+            beta,
+            gamma,
+            phi,
         )
         residuals_[t] = error
         fitted_values_[t] = fitted_value
@@ -314,7 +336,7 @@ def _numba_fit(
 
 
 @njit(fastmath=True, cache=True)
-def _predict(
+def _numba_predict(
     trend_type,
     seasonality_type,
     level,
@@ -327,11 +349,11 @@ def _predict(
 ):
     # Generate forecasts based on the final values of level, trend, and seasonals
     if phi == 1:  # No damping case
-        phi_h = 1
+        phi_h = horizon
     else:
         # Geometric series formula for calculating phi + phi^2 + ... + phi^h
         phi_h = phi * (1 - phi**horizon) / (1 - phi)
-    seasonal_index = (n_timepoints + horizon) % seasonal_period
+    seasonal_index = (n_timepoints + horizon - 1) % seasonal_period
     return _predict_value(
         trend_type,
         seasonality_type,
@@ -392,7 +414,7 @@ def _update_states(
     level,
     trend,
     seasonality,
-    data_item: int,
+    data_item,
     alpha,
     beta,
     gamma,

aeon/forecasting/tests/test_ets.py

@@ -24,7 +24,7 @@
                 seasonality_type="additive",
                 seasonal_period=4,
             ),
-            9.191190608800001,
+            11.456563248800002,
         ),
         (
             dict(
@@ -37,7 +37,7 @@
                 seasonality_type="additive",
                 seasonal_period=4,
             ),
-            16.20176819429869,
+            15.507105356706465,
         ),
         (
             dict(
@@ -50,7 +50,7 @@
                 seasonality_type="multiplicative",
                 seasonal_period=4,
             ),
-            12.301259229712382,
+            13.168538863095991,
         ),
         (
             dict(
@@ -63,7 +63,7 @@
                 seasonality_type="multiplicative",
                 seasonal_period=4,
             ),
-            16.811888294476528,
+            15.223040987015944,
         ),
     ],
 )

examples/forecasting/ets.ipynb

@@ -0,0 +1,44 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": [
+    "# ETS Forecasting\n",
+    "\n",
+    "Examples for ETS notebook here\n",
+    "\n",
+    "`aeon` has native a implementation of ETS and will soon add Auto ETS. Details on this\n",
+    " will be forthcoming when the implementation is stable"
+   ],
+   "id": "70dcc762ca5e1b6c"
+  },
+  {
+   "metadata": {},
+   "cell_type": "markdown",
+   "source": "",
+   "id": "f1fa7d726479eff9"
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}