Python Statsmodels seasonal_decompose() Guide

Time series analysis is a crucial part of data science. One common task is decomposing a time series into its components. Python's Statsmodels library provides the seasonal_decompose() function for this purpose.

This guide will explain how to use seasonal_decompose() to break down a time series into trend, seasonality, and residuals. We'll also provide example code and output for better understanding.

What is seasonal_decompose()?

The seasonal_decompose() function is part of the Statsmodels library. It decomposes a time series into three components: trend, seasonality, and residuals.

This decomposition helps in understanding the underlying patterns in the data. It is useful for forecasting, anomaly detection, and more.

How to Use seasonal_decompose()

To use seasonal_decompose(), you need to import it from the Statsmodels library. Here is a basic example:

import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt

# Sample time series data
data = [i + (i % 7) for i in range(1, 100)]
index = pd.date_range(start='2023-01-01', periods=99, freq='D')
ts = pd.Series(data, index=index)

# Decompose the time series
result = sm.tsa.seasonal_decompose(ts, model='additive')

# Plot the components
result.plot()
plt.show()

In this example, we create a simple time series with a weekly seasonality. The seasonal_decompose() function is then used to decompose the series.

Understanding the Output

The output of seasonal_decompose() includes four plots: observed, trend, seasonal, and residuals. Each plot provides insights into different aspects of the time series.

The observed plot shows the original data. The trend plot shows the long-term movement. The seasonal plot shows the repeating patterns. The residuals plot shows the remaining noise.

Parameters of seasonal_decompose()

The seasonal_decompose() function has several parameters. The most important ones are model and period.

The model parameter can be either 'additive' or 'multiplicative'. The period parameter defines the length of the seasonal cycle.

Here is an example with custom parameters:

result = sm.tsa.seasonal_decompose(ts, model='multiplicative', period=30)
result.plot()
plt.show()

In this example, we set the model to 'multiplicative' and the period to 30 days. This changes how the components are calculated and displayed.

Practical Applications

Decomposing a time series is useful in many scenarios. For example, it can help in identifying trends and seasonality in sales data. It can also be used to detect anomalies in financial data.

For more advanced analysis, you can combine seasonal_decompose() with other Statsmodels functions like VIF or Durbin-Watson Test.

Conclusion

The seasonal_decompose() function is a powerful tool for time series analysis. It helps in understanding the underlying patterns in your data. By decomposing a time series, you can make better forecasts and detect anomalies.

For more information on related topics, check out our guides on het_white() and summary().