# Pandas DataFrame: Calculate the rolling weighted window standard deviation

## Introduction

In data analysis, understanding trends and patterns is vital. One way to analyze these trends is by calculating the standard deviation over a rolling window, which can reveal the variability of a dataset within that window. However, to give more importance to certain data points, a weighted standard deviation can be employed. This tutorial will guide you through calculating the rolling weighted window standard deviation in a Pandas DataFrame, starting from the basics and moving towards more advanced techniques.

The rolling weighted window standard deviation integrates the importance of different data points based on their weights, offering a nuanced view of data variability over time. Weâ€™ll explore this using Pythonâ€™s Pandas library, a powerhouse for data manipulation and analysis.

## Getting Started

First, ensure you have Pandas installed in your environment:

``pip install pandas``

Next, import Pandas and create a simple DataFrame to work with:

``````import pandas as pd
import numpy as np
# Sample DataFrame
data = {'value': [10, 20, 30, 40, 50]}
df = pd.DataFrame(data)
print(df)``````

The output will be a simple table with one column:

``````   value
0     10
1     20
2     30
3     40
4     50``````

## Basic Rolling Standard Deviation

Before diving into weighted calculations, letâ€™s understand the basic rolling standard deviation:

``````df['rolling_std'] = df['value'].rolling(window=3).std()
print(df)``````

This will output:

``````   value  rolling_std
0     10          NaN
1     20          NaN
2     30     10.000000
3     40     10.000000
4     50     10.000000``````

As seen, the rolling standard deviation over a 3-row window provides insights into data variability.

## Calculating Weighted Rolling Standard Deviation

To calculate the weighted rolling standard deviation, we need to incorporate weights. Pandas doesnâ€™t have a built-in method for this, but we can achieve it through a custom function:

``````def weighted_rolling_std(values, weights):
weighted_mean = np.sum(weights * values) / np.sum(weights)
variance = np.sum(weights * (values - weighted_mean)**2) / np.sum(weights)
return np.sqrt(variance)

# Example usage:
window_size = 3
weights = np.array([0.5, 1, 1.5])
df['weighted_rolling_std'] = df['value'].rolling(window=window_size).apply(lambda x: weighted_rolling_std(x, weights), raw=True)
print(df)``````

This code snippet calculates the weighted rolling standard deviation over a 3-row window. The output demonstrates how incorporating weights modifies the standard deviation:

``````   value  rolling_std  weighted_rolling_std
0     10          NaN                  NaN
1     20          NaN                  NaN
2     30     10.000000           12.909944
3     40     10.000000           12.909944
4     50     10.000000           12.909944``````

## Time-Weighted Rolling Window

In many cases, your DataFrameâ€™s index may be datetime values, and you might want to weight the entries by time. Hereâ€™s how to perform a time-weighted rolling standard deviation:

``````df['date'] = pd.date_range(start='1/1/2022', periods=len(df), freq='D')
df.set_index('date', inplace=True)
# Assuming equal weights for simplicity. You can modify as needed.
df['time_weighted_roll_std'] = df['value'].rolling('3D').std()
print(df)``````

This utilizes Pandasâ€™ capability to handle rolling windows based on time, perfectly suited for time series analysis.