💡 Problem Formulation: When working with time series data, calculating the rolling mean is a common task for smoothing the data and identifying trends. Suppose you have a Pandas DataFrame, with a column of numerical data, and you desire to compute the rolling mean with a specific window size. The goal of this article is to demonstrate how to find the rolling mean in Python using Pandas, transforming the input data into a new series where each element is the calculated mean of the preceding elements defined by the window size.
Method 1: Using rolling() Function with mean()
This method involves the rolling() function provided by Pandas, which creates a Rolling object. Upon this object, you can then call the mean() method to compute the rolling mean. It’s a flexible way to specify the number of periods to use for calculating the mean, and it’s particularly effective for time-series data.
Here’s an example:
import pandas as pd
# Creating a sample DataFrame
data = pd.DataFrame({'values': [2, 4, 6, 8, 10]})
# Calculating the rolling mean with a window of 2 periods
rolling_means = data['values'].rolling(window=2).mean()
print(rolling_means)Output:
0 NaN 1 3.0 2 5.0 3 7.0 4 9.0 Name: values, dtype: float64
This code snippet creates a DataFrame with a single column and calculates the rolling mean over a window of two data points. The output shows the rolling mean, with the first value being NaN because there’s no prior data point to form a pair for the first value.
Method 2: Applying lambda Function with rolling()
The lambda function can be utilized in conjunction with the rolling() method to perform more complex rolling calculations, not just the mean. However, for the rolling mean, a lambda function serves to provide explicitness or to chain additional operations
Here’s an example:
import pandas as pd
# Creating a sample DataFrame
data = pd.DataFrame({'values': range(10)})
# Using a lambda function to calculate the rolling mean
rolling_means = data['values'].rolling(window=3).apply(lambda x: x.mean())
print(rolling_means)Output:
0 NaN 1 NaN 2 1.0 3 2.0 4 3.0 5 4.0 6 5.0 7 6.0 8 7.0 9 8.0 Name: values, dtype: float64
In this code, a lambda function is passed to apply() to calculate the rolling mean over a window of three data points. The lambda function simply calls mean() on the window elements. This can be useful for chaining complex operations within the rolling window.
Method 3: Expanding Windows
Expanding window calculations start with the first element and increase the window size until it encompasses the entire data set. The expanding() method in conjunction with mean() can be used to calculate a cumulative mean.
Here’s an example:
import pandas as pd
# Creating a sample DataFrame
data = pd.DataFrame({'values': [1, 3, 5, 7, 9]})
# Calculating the expanding mean
expanding_mean = data['values'].expanding().mean()
print(expanding_mean)Output:
0 1.0 1 2.0 2 3.0 3 4.0 4 5.0 Name: values, dtype: float64
This snippet illustrates the use of the expanding mean, which is the mean of the data up to the current point. It differs from a rolling mean in that the window size grows with each new data point.
Method 4: Weighted Rolling Mean
The weighted rolling mean assigns different weights to the observations in the window, rather than treating them equally. This can be done using the rolling() method combined with the apply() method where a custom function calculates the weighted mean.
Here’s an example:
import pandas as pd
import numpy as np
# Creating a sample DataFrame
data = pd.DataFrame({'values': range(5)})
# Define a custom function for a weighted mean
def weighted_mean(x):
weights = np.array([0.2, 0.8])
return np.dot(x, weights) / weights.sum()
# Applying the weighted mean function over a rolling window
weighted_means = data['values'].rolling(window=2).apply(weighted_mean, raw=True)
print(weighted_means)Output:
0 NaN 1 0.8 2 1.8 3 2.8 4 3.8 Name: values, dtype: float64
In this example, a custom weighted mean function is defined which applies higher weight to the more recent value in the window of two. The apply() method uses this function to compute the weighted mean for each window position.
Bonus One-Liner Method 5: Using ewm() for Exponential Weighted Moving Mean
The ewm() method in Pandas computes the exponential weighted moving average (EWMA), which gives more weight to recent observations. This method can be considered a form of weighted rolling mean where the weights decrease exponentially.
Here’s an example:
import pandas as pd
# Creating a sample DataFrame
data = pd.DataFrame({'values': range(5)})
# Calculating the exponential weighted moving mean with a span of 2
exp_weighted_mean = data['values'].ewm(span=2).mean()
print(exp_weighted_mean)Output:
0 0.000000 1 0.750000 2 1.615385 3 2.550000 4 3.520661 Name: values, dtype: float64
This one-liner demonstrates the use of the ewm() method to calculate the EWMA with a span of 2, which provides a smoother series that reacts more to recent values in the time series.
Summary/Discussion
- Method 1: Rolling Mean with
mean(). Standard approach for moving averages. Simple to use. Does not handle NaN values by default, and it requires a sufficient number of observations to fill the window. - Method 2: Rolling Mean with
lambda. Offers customizability for complex operations. Slightly more verbose. Suitable for chaining multiple operations. - Method 3: Expanding Mean. Useful for cumulative mean over time. Only requires a single data point to begin. Can be less representative of recent trends due to cumulative nature.
- Method 4: Weighted Rolling Mean. Beneficial when different weights are needed. Requires custom function for weights. More complex but allows for customization of weights.
- Method 5: Exponential Weighted Moving Mean. Great for emphasizing recent data. Reacts quickly to changes. May be too reactive for some applications depending on span.