Pandas DataFrame exponentially weighted calculations (5 examples)

Updated: February 22, 2024 By: Guest Contributor Post a comment


Performing exponentially weighted (EW) calculations with Pandas is a powerful method to apply time-dependent weights to your data, making it extremely useful for time series analysis. This tutorial will walk you through five practical examples, starting from the basics and gradually moving to more advanced applications. By understanding and using EW calculations, you can uncover deeper insights from your data, especially when handling fluctuating or seasonal trends.

Understanding Exponentially Weighted Calculations

Exponentially weighted calculations provide a way to give more importance to recent observations in a time series data. In Pandas, the ewm() method is used for such calculations, applying different types of exponentially weighted windows. These include exponentially weighted moving average (EWMA), exponentially weighted standard deviation, and more.

Example 1: Basic Exponentially Weighted Moving Average (EWMA)

Let’s begin with the most straightforward application of exponentially weighted calculations—the EWMA. We’ll start with a simple time series dataset.

import pandas as pd

data = { 'Date': ['2020-01-01', '2020-01-02', '2020-01-03', '2020-01-04'],
          'Value': [1, 2, 3, 4] }
df = pd.DataFrame(data)
df['Date'] = pd.to_datetime(df['Date'])
df.set_index('Date', inplace=True)

# Applying EWMA with a span of 2
df['EWMA'] = df['Value'].ewm(span=2).mean()

This initial example demonstrates how to apply an EWMA, with each subsequent value diminishing in weight exponentially.

Example 2: Comparing Simple and Exponentially Weighted Moving Average

Next, let’s compare the EWMA with a simple moving average (SMA) to highlight the difference in how recent values are weighted.

df['SMA'] = df['Value'].rolling(window=2).mean()
df['EWMA'] = df['Value'].ewm(span=2).mean()

# Display the DataFrame to see the comparison
df[['Value', 'SMA', 'EWMA']]

Here, you can observe how the EWMA provides a smoother curve compared to the SMA, which can be critical when analyzing time series that exhibit quick shifts in trend.

Example 3: Exponentially Weighted Volatility

Now, let’s calculate the exponentially weighted standard deviation to measure volatility over time. This can be particularly useful for financial data analysis.

df['Volatility'] = df['Value'].ewm(span=2).std()
print(df[['Value', 'Volatility']])

The output demonstrates how volatility can be captured more responsively using EW methods.

Example 4: Adjusting Alpha for Finer Control

Instead of using a fixed span, adjusting the alpha parameter allows for finer control over the exponential decay.

df['Adjusted EWMA'] = df['Value'].ewm(alpha=0.1).mean()
print(df[['Value', 'Adjusted EWMA']])

This example shows the impact of a lower alpha value, providing a less reactive EWMA that could be more suitable for data with less abrupt changes.

Example 5: Exponentially Weighted Moving Average on DataFrame with Multiple Columns

Finally, let’s apply EWMA calculations on a DataFrame with multiple columns to illustrate handling multidimensional time series data.

import numpy as np
import pandas as pd

data = np.random.rand(10, 3) * 100
cols = ['A', 'B', 'C']
df_multi = pd.DataFrame(data, columns=cols)

df_multi = df_multi.apply(lambda x: x.ewm(span=2).mean())

This advanced example efficiently demonstrates applying EW calculations across multiple data series, revealing a powerful capability of Pandas for complex datasets.


Through these examples, we’ve explored various aspects of exponentially weighted calculations in Pandas, from basic to more advanced applications. By leveraging these techniques, you can gain deeper and more nuanced insights into your time series data, aiding in more informed decision-making and analysis.