Pandas: How to perform expanding window operations on Series

Updated: February 18, 2024 By: Guest Contributor Post a comment


Pandas is a powerful and flexible Python library that provides data structures designed to make working with “relational” or “labeled” data both easy and intuitive. It aims to be the fundamental high-level building block for doing practical, real-world data analysis in Python. Among its advanced features, expanding window operations stand out for their utility in statistical and financial data analysis. An expanding window operation allows one to apply functions cumulatively over a sequence depending on the window size, which expands until it encompasses the entire series or DataFrame.

Expanding window functions are crucial for calculating cumulative statistics over a series. This might include calculating rolling means to smooth out short-term fluctuations and highlight long-term trends, or cumulative sums for running totals. This tutorial aims to elucidate how to perform expanding window operations on Series with Pandas, exhibiting the flexibility and efficiency of these operations for data analysis tasks.

Getting Started with Expanding Window Operations

First, ensure Pandas is installed and imported into your project:

import pandas as pd

Leveraging the Pandas Series, let’s commence with a simple example. Create a Series of random numbers:

data = pd.Series([4, 7, 2, 8, 1, 6, 3])

Now, let’s apply an expanding window sum operation on this series. Pandas provides the .expanding() method to execute expanding window functions,

exp_sum = data.expanding().sum()


0     4.0
1    11.0
2    13.0
3    21.0
4    22.0
5    28.0
6    31.0
Name: 0, dtype: float64

This output shows the cumulative sum of the elements as the window expands to encompass more of the series. As we advance through the series, the sum expands until it includes all elements.

Computing Moving Averages

Moving averages are commonly used to smooth data sequences to help visualize trends. The expanding window mean provides a way to compute the cumulative average that considers all preceding values. Here’s how to compute it:

exp_mean = data.expanding().mean()


0    4.000000
1    5.500000
2    4.333333
3    5.250000
4    4.400000
5    4.666667
6    4.428571
Name: 0, dtype: float64

The expanding mean starts with the first value, then includes more data points from the series to calculate an updated mean. It gradually takes all observations into account, providing a comprehensive view of the cumulative average over time.

Applying Custom Functions

Pandas is not limited to predefined operations; you can also apply custom functions to expanding windows. Suppose we want to calculate the expanding product of values. We first define our custom operation:

def expanding_product(series):
    product = series.expanding().apply(lambda x:, raw=True)
    return product

Using our initial series, let’s apply our custom expanding product function:

exp_product = expanding_product(data)


0         4.0
1        28.0
2        56.0
3       448.0
4       448.0
5      2688.0
6      8064.0
Name: 0, dtype: float64

This shows the expanding product result, cumulatively multiplying across the series as the window expands. Applying custom operations enables unique insights tailored to specific data analysis needs.

Advanced Techniques: Applying Multiple Operations

Advanced users might want to apply several operations simultaneously. This is possible by combining .aggregate() or .agg() with the expanding window. For instance, if you wish to calculate both the sum and mean:

exp_aggregate = data.expanding().agg(['sum', 'mean'])


     sum      mean
0    4.0  4.000000
1   11.0  5.500000
2   13.0  4.333333
3   21.0  5.250000
4   22.0  4.400000
5   28.0  4.666667
6   31.0  4.428571

This demonstrates the flexibility of aggregating multiple operations, which can be particularly useful for comprehensive analyses that require multiple metrics.


Expanding window operations in Pandas provide a potent tool for running cumulative calculations across a Series. As seen, this utility extends from basic sums and means to custom functions that cater to specific analytic needs. Pandas’ expanding window functionalities are vital for data analysis tasks, allowing for dynamic and detailed statistical insights into datasets.