Forecasting - Exercise¶

In [1]:
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

Dataset: Alcohol sales¶

https://fred.stlouisfed.org/series/S4248SM144NCEN Merchant Wholesalers, Except Manufacturers' Sales Branches and Offices: Nondurable Goods: Beer, Wine, and Distilled Alcoholic Beverages Sales

Load data¶

In [2]:
Y = pd.read_csv("./data/Alcohol_Sales2024.csv")
Y.head()
Out[2]:
DATE S4248SM144NCEN
0 1992-01-01 3459.0
1 1992-02-01 3458.0
2 1992-03-01 4002.0
3 1992-04-01 4564.0
4 1992-05-01 4221.0
In [3]:
Y.set_index('DATE', inplace=True)
Y.index = pd.PeriodIndex(Y.index, freq='M')
y = Y['S4248SM144NCEN']
y.head()
Out[3]:
DATE
1992-01    3459.0
1992-02    3458.0
1992-03    4002.0
1992-04    4564.0
1992-05    4221.0
Freq: M, Name: S4248SM144NCEN, dtype: float64
In [4]:
y.plot()
Out[4]:
<Axes: xlabel='DATE'>
No description has been provided for this image

Split data¶

In [5]:
from sktime.split import temporal_train_test_split
In [6]:
y_train, y_test = temporal_train_test_split(y)
y_train.shape, y_test.shape
Out[6]:
((291,), (97,))
In [7]:
y_train.plot(label='train')
y_test.plot(label='test')
plt.legend()
plt.show()
No description has been provided for this image

Exercise¶

Find the best possible forecasting model for the alcohol sales dataset in terms of MAE (mean absolute error). Remember not to use the test set for model selection.

In [8]:
from sktime.performance_metrics.forecasting import MeanAbsoluteError
from sktime.forecasting.model_evaluation import evaluate
from sktime.split import ExpandingWindowSplitter
from sktime.forecasting.model_selection import ForecastingGridSearchCV
In [9]:
mae = MeanAbsoluteError()
fh = np.arange(1, len(y_test) + 1)
cv = ExpandingWindowSplitter(fh, initial_window=96, step_length=12)
In [10]:
# how many splits?
splitted = list(cv.split(y_train))
len(splitted)
Out[10]:
9
In [11]:
fig, axs = plt.subplots(3, 3, figsize=(15, 15), sharex=True, sharey=True)
for i, (train, test) in enumerate(splitted):
    axs[i // 3, i % 3].set_title(f"Split {i}")
    y.iloc[train].plot(ax=axs[i // 3, i % 3], label='train')
    y.iloc[test].plot(ax=axs[i // 3, i % 3], label='validation')
plt.tight_layout()
plt.legend()
plt.show()
No description has been provided for this image

Naive forecasting¶

In [12]:
from sktime.forecasting.naive import NaiveForecaster

Mean¶

Cross-validation¶

In [13]:
scores_df = evaluate(NaiveForecaster(strategy="mean"), cv=cv, y=y_train, scoring=MeanAbsoluteError())
scores_df["test_MeanAbsoluteError"].mean()

/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
Out[13]:
3341.7683294975463

Performance on the test set¶

In [14]:
forecaster = NaiveForecaster(strategy="mean")
In [15]:
forecaster.fit(y_train)
Out[15]:
NaiveForecaster(strategy='mean')
Please rerun this cell to show the HTML repr or trust the notebook.
NaiveForecaster(strategy='mean')
In [16]:
y_pred = forecaster.predict(fh)

/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:400: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  if freq_from_self != freq_from_obj:
/Users/francesco/miniforge3/envs/2024_generali_ts_course_native/lib/python3.11/site-packages/sktime/forecasting/base/_fh.py:172: FutureWarning: 'M' is deprecated and will be removed in a future version, please use 'ME' instead.
  return to_offset(obj)
In [17]:
y_train.plot(label='train')
y_test.plot(label='test')
y_pred.plot(label='forecast')
plt.legend()
plt.show()
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In [18]:
mae(y_pred, y_test)
Out[18]:
6675.18213058419
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