Window functions (expanding, ewm) in Data Analysis Python

Introduction

Window functions help us look at data in small parts or over time. They let us calculate things like averages that change as we move through the data.

To see how the average of sales changes day by day in a store.

To smooth noisy data like stock prices to see trends better.

To calculate running totals or averages in a list of numbers.

To analyze time series data where recent points matter more.

To compare each data point with all previous points in order.

Syntax

Data Analysis Python

df['column'].expanding().mean()
df['column'].ewm(span=3).mean()

expanding() looks at all data from the start up to the current point.

ewm() means Exponentially Weighted Moving, which gives more weight to recent data.

Examples

This calculates the average from the first value up to each point.

Data Analysis Python

import pandas as pd

data = [1, 2, 3, 4, 5]
df = pd.DataFrame({'values': data})

# Expanding mean
exp_mean = df['values'].expanding().mean()
print(exp_mean)

This calculates a weighted average giving more importance to recent values.

Data Analysis Python

import pandas as pd

data = [1, 2, 3, 4, 5]
df = pd.DataFrame({'values': data})

# Exponentially weighted mean with span=2
ewm_mean = df['values'].ewm(span=2).mean()
print(ewm_mean)

Sample Program

This program shows how to calculate the expanding and exponentially weighted averages of sales over dates.

Data Analysis Python

import pandas as pd

# Create sample data
sales = [10, 20, 15, 30, 25]
dates = pd.date_range('2024-01-01', periods=5)
df = pd.DataFrame({'date': dates, 'sales': sales})
df.set_index('date', inplace=True)

# Calculate expanding mean of sales
expanding_avg = df['sales'].expanding().mean()

# Calculate exponentially weighted mean with span=3
ewm_avg = df['sales'].ewm(span=3).mean()

print('Expanding mean:')
print(expanding_avg)
print('\nExponentially weighted mean:')
print(ewm_avg)

Important Notes

Expanding windows always start from the first data point and grow with each step.

Exponentially weighted means react faster to recent changes than simple averages.

You can adjust the span in ewm() to control how much recent data matters.

Summary

Window functions help analyze data step-by-step or over time.

expanding() looks at all data up to now.

ewm() gives more weight to recent data for smoother trends.

Practice

1. What does the expanding() window function do in data analysis?

easy

A. Calculates statistics using a fixed-size sliding window

B. Calculates statistics using only the last 3 data points

C. Calculates statistics by giving more weight to recent data points

D. Calculates statistics using all data points up to the current one

Solution

1. Step 1: Understand expanding() function

   The expanding() function includes all data points from the start up to the current point for calculations.

2. Step 2: Compare with other window types

   Unlike rolling windows or ewm, expanding uses all past data, not a fixed window or weighted recent data.

3. Final Answer:

   Calculates statistics using all data points up to the current one -> Option D

4. Quick Check:

   expanding() = all data so far [OK]

Hint: expanding() uses all data up to now, no fixed window [OK]

Common Mistakes:

• Confusing expanding() with rolling() fixed window
• Thinking ewm() is the same as expanding()
• Assuming expanding() only uses recent data

2. Which of the following is the correct syntax to calculate the exponentially weighted mean of a pandas Series data with a span of 3?

easy

A. data.ewm(span=3).mean()

B. data.expanding(span=3).mean()

C. data.rolling(window=3).ewm().mean()

D. data.ewm(window=3).mean()

Solution

1. Step 1: Recall ewm() syntax

   The ewm() function uses parameters like span to control decay; span=3 is valid.

2. Step 2: Check each option

   data.ewm(span=3).mean() uses correct syntax: data.ewm(span=3).mean(). Others misuse parameters or combine methods incorrectly.

3. Final Answer:

   data.ewm(span=3).mean() -> Option A

4. Quick Check:

   ewm(span=3) is correct syntax [OK]

Hint: Use ewm(span=3).mean() for weighted mean with span 3 [OK]

Common Mistakes:

• Using expanding() instead of ewm() for weighted mean
• Passing window parameter to ewm() which is invalid
• Chaining rolling() before ewm() incorrectly

3. Given the pandas Series data = pd.Series([10, 20, 30, 40]), what is the output of data.expanding().mean().tolist()?

medium

A. [10.0, 15.0, 20.0, 25.0]

B. [10.0, 20.0, 30.0, 40.0]

C. [10.0, 15.0, 25.0, 35.0]

D. [10.0, 20.0, 25.0, 30.0]

Solution

1. Step 1: Calculate expanding mean step-by-step

   Expanding mean at each point is average of all values up to that index:
   Index 0: 10 / 1 = 10.0
   Index 1: (10+20)/2 = 15.0
   Index 2: (10+20+30)/3 = 20.0
   Index 3: (10+20+30+40)/4 = 25.0

2. Step 2: Match calculated list with options

   The list is [10.0, 15.0, 20.0, 25.0], which matches [10.0, 15.0, 20.0, 25.0] exactly.

3. Final Answer:

   [10.0, 15.0, 20.0, 25.0] -> Option A

4. Quick Check:

   Expanding mean averages all so far [OK]

Hint: Expanding mean averages all data up to current index [OK]

Common Mistakes:

• Calculating rolling mean instead of expanding mean
• Using last value only instead of average
• Miscomputing cumulative sums

4. You run the code data.ewm(span=2).mean() but get an error. Which fix will solve the problem?

medium

A. Import pandas as pd before using data

B. Replace span with window parameter

C. Use data.ewm(span=2).mean() on a pandas Series, not a list

D. Call mean() before ewm()

Solution

1. Step 1: Identify cause of error

   The ewm() method is a pandas Series method. If data is a plain list, it causes an error.

2. Step 2: Correct usage context

   Convert data to a pandas Series before calling ewm(), e.g., pd.Series(data).ewm(span=2).mean().

3. Final Answer:

   Use data.ewm(span=2).mean() on a pandas Series, not a list -> Option C

4. Quick Check:

   ewm() needs pandas Series [OK]

Hint: ewm() works only on pandas Series, not plain lists [OK]

Common Mistakes:

• Trying to use ewm() on Python lists
• Using wrong parameter names like window in ewm()
• Calling mean() before ewm()

5. You have daily sales data with some missing days. You want to smooth the sales trend giving more weight to recent days but still include all past data. Which pandas window function and parameter combination is best?

hard

A. data.expanding(min_periods=5).mean() to average all data after 5 days

B. data.ewm(span=5, adjust=False).mean() to weight recent days more

C. data.rolling(window=5).mean() to use last 5 days only

D. data.expanding().mean() to average all data equally

Solution

1. Step 1: Understand smoothing with weights

   To give more weight to recent days, ewm() is appropriate because it applies exponential decay.

2. Step 2: Consider missing days and all past data

   ewm() includes all past data but weights recent points more; adjust=False gives a smoother result.

3. Step 3: Compare options

   data.ewm(span=5, adjust=False).mean() to weight recent days more uses ewm(span=5, adjust=False) which fits the requirement best. Others either use equal weights or fixed windows.

4. Final Answer:

   data.ewm(span=5, adjust=False).mean() -> Option B

5. Quick Check:

   ewm() weights recent data more [OK]

Hint: Use ewm(span=5, adjust=False) for weighted smoothing with all past data [OK]

Common Mistakes:

• Using expanding() which weights all data equally
• Using rolling() which ignores older data beyond window
• Not setting adjust=False for smoother ewm