💡 Problem Formulation: When working with time series data, it’s often necessary to calculate rolling or moving statistics, such as a moving average. Such operations involve taking a subset of data points, computing a statistic, and then sliding the subset window across the data. For instance, given daily temperature readings, one might want to calculate a 7-day rolling average to smooth out daily fluctuations. The goal is to transform the input series into a new series of rolling statistics.
Method 1: Basic Rolling Window
The rolling() method in pandas is employed to create a rolling object, which can then have various statistical methods applied to it, such as mean(), sum(), or std(). By specifying the number of periods (window size), pandas calculates these statistics using a window of the given size that moves across the series.
Here’s an example:
import pandas as pd # Create a pandas Series data = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) # Calculate the rolling window with a size of 3 rolling_data = data.rolling(window=3).mean() print(rolling_data)
Output:
0 NaN 1 NaN 2 2.0 3 3.0 4 4.0 5 5.0 6 6.0 7 7.0 8 8.0 9 9.0 dtype: float64
This code snippet demonstrates how to compute the rolling mean over a Series object in pandas. Initially, the first two elements of the output are NaN because the window size is 3 and there aren’t enough data points to calculate the mean until the third element.
Method 2: Custom Window Functions
For more advanced use cases, the rolling window can be combined with the apply() function to apply a custom function to the rolling window. This is useful for when you need a rolling statistic that is not provided by pandas by default.
Here’s an example:
import pandas as pd
# Define a custom function
def calculate_range(window):
return window.max() - window.min()
# Create a pandas Series
data = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])
# Apply a custom function over the rolling window
rolling_data = data.rolling(window=4).apply(calculate_range)
print(rolling_data)Output:
0 NaN 1 NaN 2 NaN 3 3.0 4 3.0 5 3.0 6 3.0 7 3.0 8 3.0 9 3.0 dtype: float64
In this code, the custom function calculate_range() is applied to each rolling window of size 4. The function calculates the range within each window, which is the difference between the maximum and minimum value.
Method 3: Rolling Window with Offset Strings
For time series data indexed by datetime, you can specify the window size using an offset string, like ‘1D’ for one day. This method lets you handle windows of time rather than a fixed number of observations.
Here’s an example:
import pandas as pd
import numpy as np
# Create time-indexed data
date_rng = pd.date_range(start='2021-01-01', end='2021-01-10', freq='D')
data = pd.Series(np.random.randn(len(date_rng)), index=date_rng)
# Apply the rolling window with a size of '3D'
rolling_data = data.rolling('3D').mean()
print(rolling_data)Output:
2021-01-01 0.469112 2021-01-02 -0.282863 2021-01-03 -0.202020 ... other dates ... 2021-01-10 -0.561475 Freq: D, dtype: float64
The code constructs a Series with random values indexed by date. The rolling mean is then computed over a three-day sliding window, which aligns with the index’s frequency.
Method 4: Exponential Weighted Moving
An Exponential Weighted Moving (EWM) window provides exponentially decreasing weights over time, which can be useful to give more importance to more recent observations. It is specified through ewm() method rather than rolling(). Parameters such as span, halflife, and alpha determine the decay rate of the weights.
Here’s an example:
import pandas as pd # Create a pandas Series data = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) # Calculate the Exponential Weighted Moving Average ewm_data = data.ewm(span=4).mean() print(ewm_data)
Output:
0 1.000000 1 1.666667 2 2.428571 3 3.266667 4 4.161290 5 5.097561 6 6.062500 7 7.046875 8 8.040816 9 9.038462 dtype: float64
The snippet applies an exponential weighted function on the Series data, favoring more recent data points. Note how each subsequent value in the output has a considerably smaller jump compared to a regular rolling mean.
Bonus One-Liner Method 5: Rolling Aggregation with agg()
The agg() method can be used alongside rolling objects to perform multiple aggregation operations simultaneously. You can pass a list of functions or their string representations to apply them to each window.
Here’s an example:
import pandas as pd # Create a pandas Series data = pd.Series([1, 2, 3, 4, 5, 6, 7, 8, 9, 10]) # Calculate rolling aggregation with mean and standard deviation rolling_data = data.rolling(window=4).agg(['mean', 'std']) print(rolling_data)
Output:
mean std 0 NaN NaN 1 NaN NaN 2 NaN NaN 3 2.5 1.290994 ... other values ... 9 7.5 1.290994
This example uses the rolling window alongside agg() to calculate both the mean and standard deviation for each window of size 4. This is a convenient way to get multiple statistics in one go.
Summary/Discussion
- Method 1: Basic Rolling Window. Simple and effective for basic rolling statistics such as mean or sum. Limited to functions provided by pandas.
- Method 2: Custom Window Functions. Offers flexibility to apply any custom function. Might be slower due to the overhead of applying a custom function.
- Method 3: Rolling Window with Offset Strings. Ideal for time series data with datetime indices. Not suitable for non-datetime indexed data.
- Method 4: Exponential Weighted Moving. Useful for giving more weight to recent observations. Choosing appropriate parameters for weighting can be nontrivial.
- Method 5: Rolling Aggregation with
agg(). Enables simultaneous computation of multiple statistics. Can lead to more complex code if too many functions are applied at once.