Pandas – Perform expanding window calculations on DataFrame (5 examples)

Introduction

In this tutorial, we’ll delve into the power of Pandas for performing expanding window calculations on DataFrames. Expanding window calculations are an essential tool in data analysis, especially when you need to calculate cumulative statistics over a dataset. Whether you’re working in finance, data science, or any field that requires analysis of time-series data, understanding how to leverage these calculations can be invaluable.

We’ll start with some basics and gradually move to more sophisticated examples. Each example is designed to showcase a different aspect or application of expanding window calculations, complete with code snippets and outputs.

Preparing a Test DataFrame

The expanding() method in Pandas allows you to apply a function over an expanding window of values. Essentially, as you progress through your DataFrame, the window of considered rows grows from the beginning up to the current row, allowing for cumulative calculations.

import pandas as pd
import numpy as np

np.random.seed(2024)

df = pd.DataFrame({'A': np.random.rand(10)})
print(df.expanding().sum())

The above code snippet creates a DataFrame with a single column of random numbers and then applies a sum over an expanding window. The output demonstrates how each row’s value is the sum of all the preceding values including itself.

Output:

         A
0  0.588015
1  1.287123
2  1.475275
3  1.519084
4  1.724103
5  1.830166
6  2.557406
7  3.236806
8  3.710652
9  4.158948

This DataFrame will be used in the coming examples.

Example #1 – Calculating Expanding Mean

Next, let’s calculate the expanding mean. This is similar to the sum but gives us an average over the expanding window, which can be useful for smoothing out data or understanding overall trends.

df['expanding_mean'] = df.expanding().mean()
print(df)

Output:

          A  expanding_mean
0  0.588015        0.588015
1  0.699109        0.643562
2  0.188152        0.491758
3  0.043809        0.379771
4  0.205019        0.344821
5  0.106063        0.305028
6  0.727240        0.365344
7  0.679401        0.404601
8  0.473846        0.412295
9  0.448296        0.415895

This simple addition to our DataFrame adds a new column with the mean of all values up to and including the current row.

Example #2 – Expanding Window with a Minimum Number of Observations

Pandas allows you to specify a minimum number of observations that must be present before the calculation is performed. This can be especially useful in the early rows of your DataFrame, where you might want certain statistics to be calculated only when you have enough data.

df['expanding_sum_min_3'] = df.expanding(min_periods=3).sum()
print(df)

Output:

          A  expanding_sum_min_3
0  0.588015                  NaN
1  0.699109                  NaN
2  0.188152             1.475275
3  0.043809             1.519084
4  0.205019             1.724103
5  0.106063             1.830166
6  0.727240             2.557406
7  0.679401             3.236806
8  0.473846             3.710652
9  0.448296             4.158948

In the example, by setting min_periods=3, the sum is only calculated when there are at least three rows of data. This prevents early rows from having inflated or skewed results due to a lack of data.

Example #3 – Applying Custom Functions

Expanding window calculations don’t have to be limited to built-in functions. You can also apply custom functions to perform more unique computations, fitting your specific needs.

def custom_func(series):
    return series.max() - series.min()

df['expanding_custom'] = df.expanding().apply(custom_func)
print(df)

Output:

          A  expanding_custom
0  0.588015          0.000000
1  0.699109          0.111094
2  0.188152          0.510957
3  0.043809          0.655300
4  0.205019          0.655300
5  0.106063          0.655300
6  0.727240          0.683432
7  0.679401          0.683432
8  0.473846          0.683432
9  0.448296          0.683432

This example shows how to apply a custom function that calculates the range (max – min) over the expanding window. It’s a straightforward way to understand how distributions might be changing over time.

Example #4 – Handling Missing Data

Working with real-world data often means dealing with missing values. Fortunately, Pandas’ expanding functions are designed to handle NaN values gracefully. However, you should be cautious about how these NaN values affect your calculations. It’s often a good practice to either fill or drop them before applying expanding calculations.

df.fillna(method='ffill', inplace=True)  # Forward fill

df['expanding_mean'] = df.expanding().mean()
print(df)

Output:

          A  expanding_mean
0  0.588015        0.588015
1  0.699109        0.643562
2  0.188152        0.491758
3  0.043809        0.379771
4  0.205019        0.344821
5  0.106063        0.305028
6  0.727240        0.365344
7  0.679401        0.404601
8  0.473846        0.412295
9  0.448296        0.415895

Using fillna with a forward fill method ensures that NaN values do not disrupt your expanding calculations, providing a more continuous set of results.

Example #5 – Expanding Window on Multiple Columns

Finally, let’s look at how to perform expanding window calculations on multiple columns. This is particularly useful when working with datasets containing multiple features of interest.

df = pd.DataFrame({'A': np.random.rand(10), 'B': np.random.rand(10)})
df['A_expanding_sum'] = df['A'].expanding().sum()
df['B_expanding_sum'] = df['B'].expanding().sum()
print(df)

Output:

          A         B  A_expanding_sum  B_expanding_sum
0  0.019107  0.257996         0.019107         0.257996
1  0.752598  0.095542         0.771705         0.353538
2  0.602449  0.960910         1.374154         1.314448
3  0.961778  0.251767         2.335931         1.566215
4  0.664369  0.282165         3.000300         1.848380
5  0.606630  0.768254         3.606930         2.616634
6  0.449151  0.797923         4.056081         3.414557
7  0.225354  0.544037         4.281435         3.958594
8  0.670174  0.382708         4.951609         4.341302
9  0.735767  0.381651         5.687376         4.722953

This approach allows you to calculate expanding sums (or any other statistic) for multiple columns independently, providing a comprehensive view of your dataset’s cumulative properties.

Conclusion

Through these examples, we’ve seen how Pandas makes it easy to perform expanding window calculations, offering a versatile toolkit for time-series analysis. Whether you’re looking to understand cumulative sums, averages, or apply custom calculations, the expanding method provides a powerful way to analyze your data over time.