Time series decomposition helps analyze patterns in time series data. It breaks down data into trend, seasonal, and residual components. In this article, we will see how to decompose time series data in Python.

 

What is Time Series Decomposition?

 

Time series decomposition separates a time series into three distinct components:

1. Trend: The general direction in which the data moves for a long period.
2. Seasonal: The repeating short-term cycle or pattern.
3. Residual: The random noise that cannot be attributed to trend or seasonality.

Types of Time Series Decomposition Techniques

Additive Decomposition

The time series is represented as the sum of its components:

Y(t)=Trend(t)+Seasonal(t)+Residual(t)

This method is suitable when the magnitude of seasonality doesn’t change with the magnitude of the time series.

Multiplicative Decomposition

The time series is represented as the product of its components:

Y(t)=Trend(t)×Seasonal(t)×Residual(t)

This method is suitable when the magnitude of seasonality varies with the magnitude of the time series.

Methods of Decomposition

Moving Averages

Moving averages smooth out short-term fluctuations in data. They calculate the average of a fixed number of recent data points. This method highlights longer-term trends and reduces noise. Moving averages can be simple or weighted. It depends on how the data points are averaged.

Classical Decomposition

Classical decomposition separates a time series into trend, seasonal, and residual parts. In an additive model, you combine these parts by adding them together. In a multiplicative model, you combine them by multiplying them. This method helps understand and analyze the overall pattern of the time series.

Seasonal and Trend Decomposition using Loess (STL)

STL uses local regression to separate trend and seasonal components. It adapts well to data with changing seasonal patterns. STL is popular because it can handle complex time series data well.

 

Exponential Smoothing State Space Model (ETS)

The ETS method uses exponential smoothing to estimate trend and seasonal components. It gives more weight to recent data points. ETS models are good for time series with trends and seasonality. They are useful for forecasting.

Now, we will implement time series decomposition in Python.

Import Libraries

First, you must import the necessary libraries.

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

Load the data

Load your time series data into a pandas DataFrame. Let’s create a sample dataset.

# Create a sample time series data
data = {
    'Date': pd.date_range(start='2023-01-01', periods=100, freq='D'),
    'Value': np.random.randn(100) * 10 + np.linspace(10, 50, 100)
}
df = pd.DataFrame(data)
df.set_index('Date', inplace=True)

# Display the dataset
print(df)

Perform Time Series Decomposition

Use the ‘seasonal_decompose’ function from the statsmodels library to decompose the time series.

# Decompose the time series data
decomposition = seasonal_decompose(df['Value'], model='additive')

Plot the Components

Visualize the decomposed components: trend, seasonal, and residual.

# Plot the decomposed components
plt.figure(figsize=(12, 8))

plt.subplot(4, 1, 1)
plt.plot(df['Value'], label='Original Data')
plt.title('Original Time Series')
plt.legend()

plt.subplot(4, 1, 2)
plt.plot(decomposition.trend, label='Trend Component', color='orange')
plt.title('Trend Component')
plt.legend()

plt.subplot(4, 1, 3)
plt.plot(decomposition.seasonal, label='Seasonal Component', color='green')
plt.title('Seasonal Component')
plt.legend()

plt.subplot(4, 1, 4)
plt.plot(decomposition.resid, label='Residual Component', color='red')
plt.title('Residual Component')
plt.legend()

plt.tight_layout()
plt.show()

The plot divides the time series into four parts. The first subplot shows the original data. The second subplot reveals the trend. The third subplot shows seasonal patterns. The fourth subplot displays residuals. Each part provides insight into different aspects of the data.

Wrapping Up

Time series decomposition splits data into trend, seasonal, and residual parts. This helps you see the overall direction, repeating patterns, and random noise. Use time series decomposition to gain insights into your data and make smart decisions.