4  Time Series Decomposition

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from statsmodels.tsa.seasonal import STL

# Load the AirPassengers dataset
air_passengers = pd.read_csv('data/AirPassengers.csv')
air_passengers['Month'] = pd.to_datetime(air_passengers['Month'])
air_passengers.set_index('Month', inplace=True)

# Perform STL decomposition
stl = STL(air_passengers, seasonal=13)  # The seasonal parameter is chosen based on the periodicity of your data
result = stl.fit()
result

<statsmodels.tsa.seasonal.DecomposeResult at 0x1b2ffd590a0>

4.1 Method 1: Plotting

# Plot the original time series, trend, seasonal, and remainder components
fig, (ax1, ax2, ax3, ax4) = plt.subplots(4, 1, figsize=(10, 8), sharex=True)

ax1.plot(air_passengers, label='Original')
ax1.legend()

ax2.plot(result.trend, label='Trend', color='orange')
ax2.legend()

ax3.plot(result.seasonal, label='Seasonal', color='green')
ax3.legend()

ax4.plot(result.resid, label='Residual', color='red')
ax4.legend()

plt.suptitle('STL Decomposition of AirPassengers Dataset')
plt.show()

4.2 Method 2: Plotting using plotnine

from plotnine import ggplot, aes, geom_line, facet_wrap, ggtitle
# Create a DataFrame for visualization
df_visualization = pd.DataFrame({
    'Date': air_passengers.index,
    'Original': air_passengers['#Passengers'],
    'Trend': result.trend,
    'Seasonal': result.seasonal,
    'Residual': result.resid
})
df_visualization

	Date	Original	Trend	Seasonal	Residual
Month
1949-01-01	1949-01-01	112	121.463327	-9.157113	-0.306215
1949-02-01	1949-02-01	118	122.392507	0.961357	-5.353864
1949-03-01	1949-03-01	132	123.284151	12.919571	-4.203722
1949-04-01	1949-04-01	129	124.139983	4.042554	0.817463
1949-05-01	1949-05-01	121	124.967180	-3.196646	-0.770534
...	...	...	...	...	...
1960-08-01	1960-08-01	606	481.142084	132.866128	-8.008212
1960-09-01	1960-09-01	508	484.574794	25.826563	-2.401357
1960-10-01	1960-10-01	461	487.984483	-33.766745	6.782262
1960-11-01	1960-11-01	390	491.372961	-97.319814	-4.053148
1960-12-01	1960-12-01	432	494.738728	-60.351183	-2.387545

144 rows × 5 columns

# Melt the DataFrame for easier plotting
df_melted = df_visualization.melt(id_vars='Date', var_name='Component', value_name='Value')
df_melted

	Date	Component	Value
0	1949-01-01	Original	112.000000
1	1949-02-01	Original	118.000000
2	1949-03-01	Original	132.000000
3	1949-04-01	Original	129.000000
4	1949-05-01	Original	121.000000
...	...	...	...
571	1960-08-01	Residual	-8.008212
572	1960-09-01	Residual	-2.401357
573	1960-10-01	Residual	6.782262
574	1960-11-01	Residual	-4.053148
575	1960-12-01	Residual	-2.387545

576 rows × 3 columns

# Plot using plotnine
plot = (
    ggplot(df_melted, aes(x='Date', y='Value', color='Component')) +
    geom_line() +
    facet_wrap('~Component', scales='free_y') +
    ggtitle('STL Decomposition of AirPassengers Dataset')
)

# Display the plot
print(plot)

# Plot using plotnine
plot = (
    ggplot(df_melted, aes(x='Date', y='Value', color='Component')) +
    geom_line() +
    facet_wrap('~Component', scales='free_y', ncol=1) +
    ggtitle('STL Decomposition of AirPassengers Dataset')
)

# Display the plot
print(plot)

Task: Take hourly series and perform STL decomposition.