Understanding Seasonal Decomposition in Python with Statsmodels.tsa.seasonal_decompose

Seasonal decomposition is a statistical technique used to separate time series data into its trend, seasonal, and residual components. In this article, we will explore how to use the statsmodels.tsa.seasonal_decompose function in Python to perform seasonal decomposition on a given time series dataset.

Introduction to Seasonal Decomposition

Seasonal decomposition is a useful tool for analyzing time series data that exhibits periodic patterns over time. By separating the data into its trend, seasonal, and residual components, we can better understand the underlying patterns and trends in the data.

The statsmodels.tsa.seasonal_decompose function uses a symmetric moving average by default to perform seasonal decomposition. This means that if the filt argument is not specified, the frequency of the time series is inferred from the data itself.

The Problem with Missing Values

In the given example, the user asks why there are 6 NaN values in the head and tail of the trend’s series. We will now delve into the reasons behind this phenomenon.

How Seasonal Decomposition Works

The statsmodels.tsa.seasonal_decompose function takes a time series dataset as input and returns three output components:

1. trend: The linear or non-linear component that represents the overall trend in the data over time.
2. seasonal: The periodic component that represents the seasonal patterns in the data.
3. residual: The remaining component that represents the irregular or random variations in the data.

The function uses a moving average to estimate these components, with the moving average window size specified by the filt argument.

The Role of Filt Argument

As mentioned earlier, if the filt argument is not specified, the frequency of the time series is inferred from the data itself. This means that the moving average window size is automatically determined based on the pattern in the data.

However, this can lead to issues with missing values at the beginning and end of the trend’s series, as shown in the example. To avoid these issues, it is recommended to specify a fixed value for the filt argument.

Example Code

Let’s consider an example code that demonstrates how to use the statsmodels.tsa.seasonal_decompose function with and without specifying the filt argument:

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

# Create a sample time series dataset
np.random.seed(0)
data = np.random.rand(365) + 100
data_2015 = data[180:] + 200
data_2016 = data[360:] + 300

data = pd.DataFrame(data, index=pd.date_range('1/1/2014', periods=365))
data_2015 = pd.DataFrame(data_2015, index=pd.date_range('7/1/2015', periods=186))
data_2016 = pd.DataFrame(data_2016, index=pd.date_range('8/1/2016', periods=93))

# Combine the datasets
df = pd.concat([data, data_2015, data_2016], axis=0)

# Perform seasonal decomposition without specifying filt argument
decomp = seasonal_decompose(df['Value'], model='additive')

# Plot the results
trend = decomp.trend
seasonal = decomp.seasonal
residual = decomp.resid

plt.figure(figsize=(10,6))
plt.subplot(411)
plt.plot(df['Value'], label='Original')
plt.legend(loc='best')
plt.subplot(412)
plt.plot(trend, label='Trend')
plt.legend(loc='best')
plt.subplot(413)
plt.plot(seasonal, label='Seasonality')
plt.legend(loc='best')
plt.subplot(414)
plt.plot(residual, label='Residuals')
plt.legend(loc='best')
plt.tight_layout()
plt.show()

# Perform seasonal decomposition with specifying filt argument
decomp = seasonal_decompose(df['Value'], model='additive', window='h3')

# Plot the results
trend = decomp.trend
seasonal = decomp.seasonal
residual = decomp.resid

plt.figure(figsize=(10,6))
plt.subplot(411)
plt.plot(df['Value'], label='Original')
plt.legend(loc='best')
plt.subplot(412)
plt.plot(trend, label='Trend')
plt.legend(loc='best')
plt.subplot(413)
plt.plot(seasonal, label='Seasonality')
plt.legend(loc='best')
plt.subplot(414)
plt.plot(residual, label='Residuals')
plt.legend(loc='best')
plt.tight_layout()
plt.show()

Conclusion

In this article, we explored how to use the statsmodels.tsa.seasonal_decompose function in Python to perform seasonal decomposition on a given time series dataset. We discussed the reasons behind missing values at the beginning and end of the trend’s series when using the default moving average window size specified by the filt argument.

To avoid these issues, it is recommended to specify a fixed value for the filt argument. The example code provided demonstrates how to use the function with and without specifying the filt argument, as well as how to plot the results of seasonal decomposition using different moving average window sizes.

By understanding the underlying principles of seasonal decomposition and how to handle missing values, you can effectively analyze time series data and extract meaningful insights from it.

Last modified on 2023-05-25