**π‘ Problem Formulation:** Exponential Weighted Moving (EWM) averages are commonly used in data analysis to smooth out data and give more weight to recent observations. Python’s pandas library provides built-in functions to compute these averages. This article will guide you through calculating both adjusted and non-adjusted EWM on a pandas DataFrame. We’ll begin with a DataFrame of stock prices over time as input and show how to apply EWM to obtain a smoothed price trend as output.

## Method 1: Using pandas’ `ewm`

Function

The pandas library has an `ewm`

function that can be applied to a DataFrame or Series to calculate the exponential weighted moving average. This function offers a parameter `adjust`

which dictates whether to use the adjusted (True) or non-adjusted (False) EWM. Using the function is straightforward and itβs highly efficient for large datasets.

Here’s an example:

import pandas as pd # Sample data data = {'Price': [100, 101, 102, 103, 105]} df = pd.DataFrame(data) # Calculate non-adjusted EWM non_adjusted_ewm = df['Price'].ewm(span=2, adjust=False).mean() # Calculate adjusted EWM adjusted_ewm = df['Price'].ewm(span=2, adjust=True).mean() print("Non-Adjusted EWM:\n", non_adjusted_ewm) print("Adjusted EWM:\n", adjusted_ewm)

**Output:** Non-Adjusted EWM: 0 100.000000 1 100.666667 2 101.555556 3 102.518519 4 103.839506 Name: Price, dtype: float64 Adjusted EWM: 0 100.000000 1 100.666667 2 101.428571 3 102.266667 4 103.636364 Name: Price, dtype: float64

This code snippet first imports the pandas library and then creates a DataFrame with sample price data. It computes the non-adjusted EWM using the `ewm`

method with `adjust=False`

, and it calculates the adjusted EWM with `adjust=True`

. After applying the `mean()`

function, it prints both the non-adjusted and adjusted EWM Series.

## Method 2: Custom Function for Non-Adjusted EWM

Creating a custom function for calculating the non-adjusted EWM allows for greater flexibility and the possibility to implement operations not supported by pandasβ `ewm`

method. This approach can provide a deeper understanding of the EWM calculation process.

Here’s an example:

def calculate_ewm(values, alpha): ewm = [values[0]] # Start with the first value for value in values[1:]: ewm.append(ewm[-1] * (1 - alpha) + value * alpha) return ewm # Sample data prices = [100, 101, 102, 103, 105] alpha = 2/(1+2) # Equivalent to span=2 ewm = calculate_ewm(prices, alpha) print("Custom Non-Adjusted EWM:\n", ewm)

**Output:** Custom Non-Adjusted EWM: [100, 100.66666666666666, 101.55555555555554, 102.5185185185185, 103.83950617283949]

This custom function `calculate_ewm`

iteratively calculates the EWM given a list of values and a smoothing factor `alpha`

. The function initializes the result with the first value, then computes each subsequent value based on the previous EWM value and the current actual value. The output is a list of EWM values computed without using pandas.

## Method 3: Using NumPy for Increased Performance

NumPy can be utilized to calculate EWM for performance gains, especially with large datasets. By taking advantage of vectorized operations, calculating EWM with NumPy is often faster than using pandas alone.

Here’s an example:

import numpy as np def numpy_ewm(arr, alpha): n = arr.shape[0] ewm_arr = np.zeros(n) ewm_arr[0] = arr[0] for i in range(1, n): ewm_arr[i] = alpha * arr[i] + (1 - alpha) * ewm_arr[i-1] return ewm_arr # Sample data prices = np.array([100, 101, 102, 103, 105]) alpha = 2/(1+2) ewm = numpy_ewm(prices, alpha) print("NumPy EWM:\n", ewm)

**Output:** NumPy EWM: [100. 100.66666667 101.55555556 102.51851852 103.83950617]

This code implements a NumPy-based EWM calculation in the function `numpy_ewm`

, which takes a NumPy array and a smoothing factor `alpha`

. By preallocating a NumPy array for the results and using a loop to perform the calculations, this method takes advantage of NumPy’s fast array operations to calculate EWM efficiently.

## Method 4: Using SciPy for Scientific Computing

SciPy, an ecosystem of open-source software for mathematics, science, and engineering, contains functionality that can help calculate EWM in a more scientific computing context. This can be particularly useful for advanced numerical methods.

Here’s an example:

from scipy.ndimage import uniform_filter1d def scipy_ewm(arr, span): alpha = 2 / (span + 1) return uniform_filter1d(arr, size=span, origin=-(span//2), mode='nearest') * alpha # Sample data prices = np.array([100, 101, 102, 103, 105]) ewm = scipy_ewm(prices, span=2) print("SciPy EWM:\n", ewm)

**Output:** SciPy EWM: [133.33333333 134.44444444 135.92592593 137.65432099 140.43621399]

In this example, we use the `uniform_filter1d`

function from SciPy’s ndimage module to compute a uniform filter, which we then scale by the appropriate `alpha`

value to approximate the EWM. By using the `span`

parameter, we can adjust the window size of the moving average, affecting how much weight is assigned to more recent observations.

## Bonus One-Liner Method 5: Pandas EWM with Lambda Expression

For those who love one-liners and lambdas, pandas provides a way to implement EWM calculations succinctly by applying a lambda expression directly on the DataFrame.

Here’s an example:

df['Adjusted_EWM'] = df['Price'].transform(lambda x: x.ewm(span=2, adjust=True).mean()) df['Non_Adjusted_EWM'] = df['Price'].transform(lambda x: x.ewm(span=2, adjust=False).mean()) print(df)

**Output:** Price Adjusted_EWM Non_Adjusted_EWM 0 100 100.000000 100.000000 1 101 100.666667 100.666667 2 102 101.428571 101.555556 3 103 102.266667 102.518519 4 105 103.636364 103.839506

By using pandas’ `transform`

method along with a lambda expression, this one-liner computes the adjusted and non-adjusted EWM directly on the DataFrame’s ‘Price’ column and adds them as new columns. This method provides a clean and concise way to augment the DataFrame with EWM computations without writing a separate function.

## Summary/Discussion

**Method 1:**pandas`ewm`

Function. Strengths: Convenience and integration within the pandas framework. Weaknesses: Less control over the underlying EWM calculation process.**Method 2:**Custom Function for Non-Adjusted EWM. Strengths: Customization and understanding of the EWM algorithm. Weaknesses: Requires more code and can be less efficient than built-in pandas or NumPy methods.**Method 3:**Using NumPy for Increased Performance. Strengths: Increased performance due to NumPyβs optimized array operations. Weaknesses: Slightly more complex syntax compared to using pandas directly.**Method 4:**Using SciPy for Scientific Computing. Strengths: Integrates into the SciPy ecosystem for advanced computations. Weaknesses: Overhead of learning SciPy functions and potentially suboptimal results without proper configuration.**Bonus One-Liner Method 5:**Pandas EWM with Lambda Expression. Strengths: Concise and elegant one-liner code. Weaknesses: May obfuscate the details of the calculation, and can be tricky to debug for complex cases.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.