# Pandas DataFrame: Calculate the Rolling Weighted Window Sum

## Introduction

Working with time-series data often requires the application of various statistical operations to understand trends and patterns. One such operation is the calculation of a rolling weighted sum, which can provide insights by considering recent values more heavily than older ones. This tutorial will guide you through using Pandas to calculate the rolling weighted window sum on DataFrame objects. We will start with the basics and progressively dive into more advanced examples.

## Getting Started

Before diving into the examples, make sure you have Pandas installed in your Python environment. If not, you can install it by running:

``````pip install pandas
``````

Assuming you have Pandas installed, the first step is to import Pandas:

``````import pandas as pd
``````

## Basic Example

Letâ€™s start with a basic example where we calculate a simple rolling window sum, upon which we will build more complex calculations:

``````data = {'values': [1, 2, 3, 4, 5]}
df = pd.DataFrame(data)
df['rolling_sum'] = df['values'].rolling(window=3).sum()
print(df)
``````

Output:

``````   values  rolling_sum
0       1          NaN
1       2          NaN
2       3          6.0
3       4         10.0
4       5         12.0
``````

## Introduction to Weighted Rolling Window

A weighted rolling window assigns different weights to different values in the window, typically giving more importance to recent values. To calculate a weighted rolling window sum in Pandas, we use the `apply()` function along with a custom weighting function.

## Creating a Simple Weight Function

Letâ€™s implement a simple linear weight function where weights increase linearly with time:

``````def linear_weight(array):
weights = np.linspace(1, len(array), num=len(array))
return np.dot(weights, array) / weights.sum()
``````

This function calculates the sum of the product of each element in the array and its weight and then divides by the total sum of weights. Note, you need to import numpy:

``````import numpy as np
``````

## Applying Weighted Rolling Window

Now, letâ€™s apply this function to our DataFrame:

``````df['weighted_rolling_sum'] = df['values'].rolling(window=3).apply(linear_weight, raw=True)
print(df)
``````

Output:

``````   values  rolling_sum  weighted_rolling_sum
0       1          NaN                   NaN
1       2          NaN                   NaN
2       3          6.0             10.666667
3       4         10.0             12.333333
4       5         12.0             14.000000
``````

As we delve further, itâ€™s interesting to explore more complex weighting schemes, such as exponential weighting. Pandas includes an efficient function for this called `ewm()`, which stands for Exponential Weighted Moving.

## Exponential Weighted Window

Hereâ€™s how you can apply an exponential weighted window sum:

``````df['exp_weighted_sum'] = df['values'].ewm(span=3).mean()
print(df)
``````

Output:

``````   values  rolling_sum  weighted_rolling_sum  exp_weighted_sum
0       1          NaN                   NaN          1.000000
1       2          NaN                   NaN          1.666667
2       3          6.0             10.666667          2.428571
3       4         10.0             12.333333          3.266667
4       5         12.0             14.000000          4.161290
``````

This output illustrates how recent values are given more weight, and the resulting sum adjusts more quickly to changes in the data.

## Conclusion

Calculating the rolling weighted window sum using Pandas provides a powerful method to analyze time-series data, highlight trends, and smooth out noise. Whether using simple linear weights or applying exponential weighting, Pandas offers the tools needed to conduct these analyses efficiently. As weâ€™ve seen through these examples, implementing these calculations is straightforward, allowing researchers and analysts to focus more on insights than on the intricacies of the calculation implementations.

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