Séries Temporelles et Prévision avec Python

from statsmodels.tsa.stattools import adfuller

result = adfuller(serie)
print(f"p-value ADF : {result[1]:.4f}")
# p-value < 0.05 → série stationnaire

from statsmodels.tsa.seasonal import seasonal_decompose
import pandas as pd, numpy as np

dates = pd.date_range("2022-01-01", periods=104, freq="W")
values = 50 + np.arange(104) * 0.3 + 10 * np.sin(np.arange(104) * 2 * np.pi / 52) + np.random.normal(0, 2, 104)
serie = pd.Series(values, index=dates)

decomposition = seasonal_decompose(serie, model="additive", period=52)
# decomposition.trend    → tendance lissée
# decomposition.seasonal → pattern saisonnier
# decomposition.resid    → résidu (bruit)

from statsmodels.tsa.arima.model import ARIMA

model = ARIMA(serie, order=(2, 1, 1))  # p=2, d=1, q=1
result = model.fit()
forecast = result.forecast(steps=12)

from prophet import Prophet
import pandas as pd, numpy as np

# Données simulées : ventes quotidiennes
dates = pd.date_range("2024-01-01", periods=365, freq="D")
sales = (100
         + np.arange(365) * 0.2
         + 20 * np.sin(np.arange(365) * 2 * np.pi / 7)
         + np.random.normal(0, 5, 365))

df = pd.DataFrame({"ds": dates, "y": sales})

model = Prophet(yearly_seasonality=False, weekly_seasonality=True)
model.fit(df)

future   = model.make_future_dataframe(periods=30)
forecast = model.predict(future)

print(forecast[["ds", "yhat", "yhat_lower", "yhat_upper"]].tail(5))

import pandas as pd, numpy as np
from xgboost import XGBRegressor

def create_features(df):
    df = df.copy()
    df["day_of_week"] = df.index.dayofweek
    df["month"]       = df.index.month
    df["lag_1"]       = df["y"].shift(1)
    df["lag_7"]       = df["y"].shift(7)
    df["rolling_7"]   = df["y"].shift(1).rolling(7).mean()
    return df.dropna()

df_feat = create_features(df.set_index("ds"))
X = df_feat.drop("y", axis=1)
y = df_feat["y"]

model = XGBRegressor(n_estimators=200, learning_rate=0.05, max_depth=4)
model.fit(X, y)

from sklearn.model_selection import TimeSeriesSplit
from sklearn.metrics import mean_absolute_error
import numpy as np

tscv = TimeSeriesSplit(n_splits=5)
scores = []

for fold, (train_idx, test_idx) in enumerate(tscv.split(X)):
    X_tr, X_te = X.iloc[train_idx], X.iloc[test_idx]
    y_tr, y_te = y.iloc[train_idx], y.iloc[test_idx]
    model.fit(X_tr, y_tr)
    mae = mean_absolute_error(y_te, model.predict(X_te))
    scores.append(mae)
    print(f"Fold {fold+1} MAE : {mae:.2f}")

print(f"\nMAE moyen : {np.mean(scores):.2f} ± {np.std(scores):.2f}")