Calculating Expanding Z-Score Across Multiple Columns Using Pandas and Groupby Operations

Pandas - Expanding Z-Score Across Multiple Columns

Calculating an expanding z-score for time series data can be a useful technique in finance, economics, and other fields where time series analysis is prevalent. However, when dealing with multiple columns of data that are all time series in nature, calculating the z-scores for each column separately is not sufficient. Instead, we want to calculate the expanding z-score across all columns simultaneously.

In this article, we’ll explore how to achieve this using pandas and groupby operations. We’ll start by examining the problem, providing example data, and then discuss potential solutions before diving into code.

Background

When working with time series data in pandas, it’s common to calculate the mean and standard deviation of a column over some period (e.g., day, week, month). However, when dealing with multiple columns, we often want to pool their values together. This can be done using various groupby operations.

One approach is to use the groupby function on the index and then apply an aggregation function like mean or std. Another approach is to use the stack method to transform the DataFrame into a long format and then aggregate along the columns axis.

In this article, we’ll explore both of these approaches and discuss their strengths and weaknesses. We’ll also introduce the concept of expanding z-scores, which will help us choose the most suitable approach for our problem.

Example Data

Let’s start with some example data to illustrate the problem:

import pandas as pd
import numpy as np
np.random.seed(42)

df = pd.DataFrame(np.random.rand(5,5),
                  columns=list('ABCDE'),
                  index=pd.date_range('2016-12-31', periods=5))

df.index.name = 'DATE'

This DataFrame has five time series columns (A, B, C, D, E) and a date index. We want to calculate an expanding z-score for each column, but instead of calculating the mean and standard deviation within each column separately, we want to pool all columns together.

Potential Solutions

Now that we have our example data, let’s discuss some potential solutions:

Approach 1: Using `groupby` Operation

One approach is to use a groupby operation on the index and then apply an aggregation function like mean or std. We can do this by first grouping the DataFrame by the date index and then applying the desired aggregation function.

df_grouped = df.groupby(df.index)[list('ABCDE')].mean()

This will give us a new DataFrame with the mean of each column for each date. However, we want to calculate an expanding z-score, which means we need to look at the values over time.

Approach 2: Using `stack` Operation

Another approach is to use the stack method to transform the DataFrame into a long format and then aggregate along the columns axis.

df_stacked = df.stack()

This will give us a new Series with all the column values stacked together. We can then apply an aggregation function like mean or std.

Approach 3: Using `expanding` Operation

Finally, we can use the expanding operation to create a new DataFrame with the expanding z-score.

df_expanding = df.expanding(2)

This will give us a new DataFrame with the values over time. We can then apply an aggregation function like mean or std.

However, these approaches have limitations. The first approach doesn’t take into account the values across all columns simultaneously, while the second approach transforms the entire DataFrame into a long format, which may not be desirable.

Combining Columns in `expanding` Operation

To calculate an expanding z-score that pools all columns together, we need to use the expanding operation with a combination of groupby and aggregations. One way to do this is by using the groupby function on the index and then applying an aggregation function like mean or std.

Here’s how you can combine columns in an expanding operation:

def pooled_expanding_zscore(df, min_periods):
    # groupby the date index
    df_grouped = df.groupby(df.index)[list('ABCDE')].mean()
    
    # expand the dataframe
    df_expanded = df_grouped.ewm(alpha=0, adjust=False).mean()  # default is alpha=0
    
    # add min_periods to kill off early rows
    if min_periods > 1:
        df_expanded.iloc[:min_periods-1,:] = np.nan

    return df_expanded

This will give us a new DataFrame with the mean of each column for each date, which can then be used as input for calculating an expanding z-score.

Calculating Expanding Z-Score

To calculate an expanding z-score, we need to divide the values by their respective standard deviations. We can do this using the following code:

def pooled_expanding_zscore(df):
    # combine columns into a matrix
    df_mat = df.loc[:,list('ABCDE')].as_matrix()
    
    # calculate mean and std for each column
    exp_mean_mat = df_mat.mean(axis=0, keepdims=True)
    exp_std_mat = df_mat.std(axis=0, keepdims=True)

    # calculate z-score
    zScores = (df_mat - exp_mean_mat) / exp_std_mat

    return pd.DataFrame(zScores, index=df.index, columns=list('ABCDE'))

This will give us a new DataFrame with the expanding z-scores for each column.

Conclusion

Calculating an expanding z-score for multiple columns of time series data can be achieved using various approaches. By combining groupby operations and aggregations, we can create a new DataFrame with the expanding z-score that pools all columns together. This approach provides a flexible way to calculate z-scores across multiple columns, which is essential in many fields where time series analysis is prevalent.

We hope this article has provided you with an overview of how to achieve this using pandas and groupby operations. If you have any questions or need further clarification, feel free to ask!

Last modified on 2024-09-25