Prophet

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import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from prophet import Prophet

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date = pd.date_range("2020-01-01", periods=365, freq="D")

# Target variable for forecasting
y = [
    np.cos(di.weekday())
    + di.month % 2 / 2
    + np.log(i + 1) / 3.0
    + np.random.rand() / 10
    for i, di in enumerate(date)
]

# Trend component
x = [18627 + i - 364 for i in range(365)]
trend_y = [np.log(i + 1) / 3.0 for i, di in enumerate(date)]
weekly_y = [np.cos(di.weekday()) for i, di in enumerate(date)]
seasonal_y = [di.month % 2 / 2 for i, di in enumerate(date)]
noise_y = [np.random.rand() / 10 for i in range(365)]

df = pd.DataFrame({"ds": date, "y": y})
df.index = date

# Data used in the experiment
plt.title("Sample Data")
sns.lineplot(data=df)
plt.show()

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plt.figure(figsize=(14, 6))
plt.title("Decomposing y into its components")
plt.subplot(511)
plt.plot(x, trend_y, "-.", color="red", label="Trend", alpha=0.9)
plt.subplot(512)
plt.plot(x, weekly_y, "-.", color="green", label="Periodic Fluctuation (Weekly)", alpha=0.9)
plt.subplot(513)
plt.plot(x, seasonal_y, "-.", color="orange", label="Periodic Fluctuation (Monthly)", alpha=0.9)
plt.subplot(514)
plt.plot(x, noise_y, "-.", color="k", label="Noise Component")
plt.subplot(515)
sns.lineplot(data=df)
plt.show()

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def train_and_forecast_pf(
    data,
    periods=90,
    yearly_seasonality=False,
    weekly_seasonality=True,
    daily_seasonality=True,
):
    """Train a Prophet model and forecast future values.

    Args:
        data (pandas.DataFrame): Time series data.
        periods (int, optional): Length of the forecast period. Defaults to 90.
        yearly_seasonality (bool, optional): Whether annual seasonality is present. Defaults to False.
        weekly_seasonality (bool, optional): Whether weekly seasonality is present. Defaults to True.
        daily_seasonality (bool, optional): Whether daily seasonality is present. Defaults to True.

    Returns:
        _type_: Forecast model, forecast results.
    """
    assert "ds" in data.columns and "y" in data.columns, "The input data must contain 'ds' and 'y' columns."
    # Train the model
    m = Prophet(
        yearly_seasonality=yearly_seasonality,
        weekly_seasonality=weekly_seasonality,
        daily_seasonality=daily_seasonality,
    )
    m.fit(df)

    # Make future predictions
    future = m.make_future_dataframe(periods=periods)
    forecast = m.predict(future)
    return m, forecast

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# Check the forecast results
periods = 90
m, forecast = train_and_forecast_pf(
    df,
    periods=periods,
    yearly_seasonality=False,
    weekly_seasonality=True,
    daily_seasonality=True,
)
fig = m.plot(forecast)
plt.title("Prophet Forecast Results")
plt.axvspan(18627, 18627 + periods, color="coral", alpha=0.4, label="Forecast Period")
plt.legend()
plt.show()

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# Check the forecast results
periods = 90
m, forecast = train_and_forecast_pf(
    df,
    periods=periods,
    yearly_seasonality=False,
    weekly_seasonality=True,
    daily_seasonality=True,
)
fig = m.plot(forecast)
plt.title("Prophet Forecast Results")
plt.axvspan(18627, 18627 + periods, color="coral", alpha=0.4, label="Forecast Period")
plt.legend()
plt.show()