Seasonal Decomposition | Time Series Analysis

Introduction

Seasonal decomposition is a method used in time series analysis to break down a series into its constituent components: trend, seasonal, and residual components. This is particularly useful for understanding the underlying patterns and making accurate forecasts.

Components of Time Series

A typical time series can be decomposed into three components:

Trend: The long-term progression of the series.
Seasonal: The repeating short-term cycle in the series.
Residual: The random variation that remains after removing the trend and seasonal components.

Types of Seasonal Decomposition

There are primarily two types of seasonal decomposition methods:

Additive Decomposition: Suitable when the seasonal variation is roughly constant through the series.
Multiplicative Decomposition: Suitable when the seasonal variation changes proportional to the level of the series.

Using Python for Seasonal Decomposition

Python's statsmodels library provides an easy-to-use function for seasonal decomposition. Below is a step-by-step guide.

Step 1: Install Required Libraries

First, ensure you have the necessary libraries installed. You can install them using pip:

pip install pandas statsmodels matplotlib

Step 2: Load the Data

Load your time series data into a Pandas DataFrame. For this example, we'll use a sample dataset.

import pandas as pd
import matplotlib.pyplot as plt

# Sample data
data = {
    'Date': pd.date_range(start='2020-01-01', periods=24, freq='M'),
    'Value': [112, 118, 132, 129, 121, 135, 148, 148, 136, 119, 104, 118, 115, 126, 141, 135, 125, 149, 170, 170, 158, 133, 114, 140]
}
df = pd.DataFrame(data)
df.set_index('Date', inplace=True)
df.head()

Step 3: Perform Seasonal Decomposition

Use the seasonal_decompose function from the statsmodels library to perform the decomposition.

from statsmodels.tsa.seasonal import seasonal_decompose

# Perform decomposition
decomposition = seasonal_decompose(df['Value'], model='multiplicative', period=12)

# Plot the decomposition
fig = decomposition.plot()
plt.show()

Step 4: Interpret the Results

The decomposition plot will show the observed, trend, seasonal, and residual components. Here's an example output:

Each component helps in understanding the underlying patterns of the time series data:

Observed: The original time series data.
Trend: The long-term movement in the data.
Seasonal: The repeating short-term cycle.
Residual: The noise or random variation in the data.

Conclusion

Seasonal decomposition is a powerful tool for time series analysis. By breaking down a series into its trend, seasonal, and residual components, we can gain deeper insights and make more accurate forecasts.

Seasonal Decomposition - Time Series Analysis