11_window_functions

Window Functions

Description: Window functions allow for calculations over a defined window or range of data points, useful for time-series analysis and moving averages.

• DataFrame.rolling(): Applies a rolling window calculation to DataFrame data.
• DataFrame.expanding(): Applies an expanding window calculation to DataFrame data.
• DataFrame.ewm(): Applies an exponentially weighted window calculation to DataFrame data.

DataFrame.rolling()

Explanation: The DataFrame.rolling() function provides rolling window calculations for a DataFrame. It allows you to compute statistics over a moving window of a specified size, which is particularly useful for time series analysis and smoothing.

Features:

• Rolling Window: Applies calculations over a fixed-size window that moves through the data.
• Flexibility: Supports various window functions such as mean, sum, and custom functions.
• Adjustable Parameters: Allows customization of window size and other settings.

Problem Solved:

• Useful for smoothing data, calculating moving averages, and other rolling statistics in time series analysis.

Parameters:

• window: Size of the moving window. Can be an integer specifying the number of observations, or a string for time-based windows (e.g., '7D' for 7 days).
• min_periods: Minimum number of observations in the window required to have a value. Default is None.
• center: Boolean indicating whether the window should be centered around the current data point. Default is False.
• axis: Axis to apply the function along. Default is 0 (rows).

Example Code:

import pandas as pd

# Sample DataFrame with numerical data
data = {
    'Date': pd.date_range(start='2024-01-01', periods=10, freq='D'),
    'Values': [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
}
df = pd.DataFrame(data)
df.set_index('Date', inplace=True)

# Calculating rolling mean with a window of 3 days
rolling_mean = df.rolling(window=3).mean()

# Displaying the result
print("Rolling Mean:")
print(rolling_mean)

Explanation:

• df.rolling(window=3).mean() calculates the rolling mean of the 'Values' column over a 3-day window.

DataFrame.expanding()

Explanation: The DataFrame.expanding() function provides expanding window calculations. Unlike the rolling window, the expanding window grows as more data points are included, from the start to the current data point.

Features:

• Expanding Window: Computes statistics from the start of the DataFrame up to the current point.
• Accumulation: Suitable for cumulative calculations.

Problem Solved:

• Useful for computing cumulative statistics such as cumulative sums or means over time.

Parameters:

• axis: Axis to apply the function along. Default is 0 (rows).

Example Code:

import pandas as pd

# Sample DataFrame with numerical data
data = {
    'Values': [1, 2, 3, 4, 5]
}
df = pd.DataFrame(data)

# Calculating expanding mean
expanding_mean = df.expanding().mean()

# Displaying the result
print("Expanding Mean:")
print(expanding_mean)

Explanation:

• df.expanding().mean() calculates the expanding mean from the start of the data up to each data point.

DataFrame.ewm()

Explanation: The DataFrame.ewm() function provides exponential weighted calculations. It applies an exponentially decreasing weight to the observations, giving more importance to recent observations.

Features:

• Exponential Weighting: Applies weights that decrease exponentially, which is useful for time series data with trends.
• Customizable: Allows customization of the span, halflife, or alpha for exponential weighting.

Problem Solved:

• Useful for smoothing time series data and calculating exponentially weighted moving averages or other statistics.

Parameters:

• com: Center of mass for exponential weighting (1 / alpha - 1).
• span: Span for the exponential weighting.
• halflife: Half-life for the exponential weighting.
• alpha: Smoothing factor.
• adjust: Boolean indicating whether to adjust the weights (default True).

Example Code:

import pandas as pd

# Sample DataFrame with numerical data
data = {
    'Values': [10, 20, 30, 40, 50]
}
df = pd.DataFrame(data)

# Calculating exponentially weighted mean with a span of 2
ewm_mean = df.ewm(span=2).mean()

# Displaying the result
print("Exponentially Weighted Mean:")
print(ewm_mean)

Explanation:

• df.ewm(span=2).mean() calculates the exponentially weighted mean with a span of 2.