ewm() for exponential moving average in Pandas - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of ewm() with span parameter

What is the output of the following code snippet?

Pandas

import pandas as pd
s = pd.Series([10, 20, 30, 40, 50])
ewm_result = s.ewm(span=3, adjust=False).mean()
print(ewm_result.round(2))

A [10.00, 15.00, 22.50, 31.25, 40.62]

B [10.00, 13.33, 19.44, 27.78, 37.96]

C [10.00, 20.00, 30.00, 40.00, 50.00]

D [10.00, 16.67, 25.56, 35.37, 45.91]

💡 Hint

Remember that adjust=False means the weights are calculated recursively without adjusting for prior weights.

With span=3 and adjust=False, the ewm() calculates the exponential moving average giving more weight to recent values. The output is a series of smoothed values starting at the first value.

❓ data_output

intermediate

Number of items in ewm result with min_periods

How many non-NaN values are in the result of this code?

Pandas

import pandas as pd
s = pd.Series([5, 10, 15, 20, 25])
ewm_result = s.ewm(span=2, min_periods=3).mean()
print(ewm_result.dropna().count())

A 3

B 2

C 5

D 0

💡 Hint

min_periods sets the minimum number of observations required to have a value.

Since min_periods=3, the first two values are NaN. From the third value onward, the ewm mean is calculated, so 3 values are non-NaN.

🔧 Debug

advanced

Identify the error in ewm() usage

What error does this code raise?

Pandas

import pandas as pd
s = pd.Series([1, 2, 3, 4])
ewm_result = s.ewm(com=0, span=2).mean()

A No error, runs successfully

B TypeError: ewm() got multiple values for argument 'span'

C ValueError: com and span cannot be specified at the same time

D AttributeError: 'Series' object has no attribute 'ewm'

💡 Hint

Check the parameters passed to ewm().

You cannot specify both 'com' and 'span' parameters together in ewm(). This raises a ValueError.

🚀 Application

advanced

Using ewm() to smooth noisy data

You have a noisy time series data. Which ewm() parameter setting will give the smoothest result?

A halflife=1, adjust=True

B span=10, adjust=True

C span=2, adjust=False

D com=0.5, adjust=False

💡 Hint

A larger span means more smoothing.

A larger span (10) with adjust=True gives more weight to all past data, resulting in smoother output.

🧠 Conceptual

expert

Effect of adjust parameter in ewm()

Which statement best describes the effect of adjust=False in pandas ewm()?

A Weights are normalized so the sum equals 1, considering all past data.

B The ewm() function raises an error if adjust=False is used.

C The result is a simple moving average ignoring weights.

D Weights are calculated recursively without normalization, giving more weight to recent data.

💡 Hint

Think about how weights are applied when adjust=False.

With adjust=False, the calculation uses recursive weights without normalizing over all past data, emphasizing recent points more.

Practice

1. What does the ewm() function in pandas primarily do?

easy

A. Sorts the data in ascending order

B. Calculates the simple moving average with equal weights

C. Calculates the exponential moving average giving more weight to recent data points

D. Removes missing values from the dataset

Solution

1. Step 1: Understand the purpose of ewm()

   The ewm() function is used to calculate exponential weighted functions, mainly the exponential moving average (EMA), which gives more importance to recent data points.

2. Step 2: Compare with other options

   Simple moving average uses equal weights, sorting and removing missing values are unrelated to ewm().

3. Final Answer:

   Calculates the exponential moving average giving more weight to recent data points -> Option C

4. Quick Check:

   ewm() = exponential moving average [OK]

Hint: Remember: ewm() weights recent data more [OK]

Common Mistakes:

• Confusing ewm() with simple moving average
• Thinking ewm() sorts data
• Assuming ewm() removes missing values

2. Which of the following is the correct syntax to calculate the exponential moving average with a span of 3 on a pandas Series data?

easy

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

B. data.ewm(3).mean()

C. data.ewm(span=3).sum()

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

Solution

1. Step 1: Identify correct parameter usage in ewm()

   The span parameter sets the decay in ewm(). It must be named explicitly as span=3.

2. Step 2: Confirm correct method to get EMA

   Calling mean() after ewm() computes the exponential moving average. Using sum() or unnamed parameters is incorrect.

3. Final Answer:

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

4. Quick Check:

   Use span=3 and mean() [OK]

Hint: Use span= for decay, then call mean() [OK]

Common Mistakes:

• Omitting parameter name for span
• Using sum() instead of mean()
• Using window parameter instead of span

3. Given the pandas Series data = pd.Series([10, 20, 30, 40]), what is the output of data.ewm(span=2).mean()?

medium

A. [10.0, 20.0, 30.0, 40.0]

B. [10.0, 15.0, 25.0, 35.0]

C. [10.0, 18.0, 26.4, 36.16]

D. [10.0, 16.67, 25.56, 35.19]

Solution

1. Step 1: Calculate alpha from span

   Alpha = 2 / (span + 1) = 2 / (2 + 1) = 0.6667 approximately.

2. Step 2: Compute EMA step-by-step

   EMA_0 = 10.0
   EMA_1 = 0.6667*20 + 0.3333*10 ≈ 16.67
   EMA_2 = 0.6667*30 + 0.3333*16.67 ≈ 25.56
   EMA_3 = 0.6667*40 + 0.3333*25.56 ≈ 35.19

3. Final Answer:

   [10.0, 16.67, 25.56, 35.19] -> Option D

4. Quick Check:

   EMA with span=2 = [10.0, 16.67, 25.56, 35.19] [OK]

Hint: Calculate alpha = 2/(span+1), then apply EMA formula [OK]

Common Mistakes:

• Using simple average instead of EMA
• Wrong alpha calculation
• Not applying weights correctly

4. What is wrong with this code snippet to calculate EMA?

import pandas as pd
data = pd.Series([1, 2, 3, 4])
ema = data.ewm(span=3).mean

medium

A. span parameter should be an integer, not 3

B. Missing parentheses after mean to call the function

C. ewm() does not accept span parameter

D. Series data must be converted to DataFrame first

Solution

1. Step 1: Check method call syntax

   The code assigns mean without parentheses, so it assigns the method itself, not the result.

2. Step 2: Confirm correct usage of mean()

   To get EMA values, mean() must be called with parentheses: mean().

3. Final Answer:

   Missing parentheses after mean to call the function -> Option B

4. Quick Check:

   Call mean() with () to get EMA [OK]

Hint: Always call mean() with parentheses to compute EMA [OK]

Common Mistakes:

• Forgetting parentheses after mean
• Misunderstanding span parameter type
• Thinking ewm() needs DataFrame

5. You have daily sales data in a pandas DataFrame df with a column 'sales'. You want to smooth the sales data giving more importance to recent days but also want to limit the influence of very old data. Which ewm() parameter should you adjust to control how fast the weights decrease?

hard

A. span

B. min_periods

C. adjust

D. ignore_na

Solution

1. Step 1: Understand the role of span in ewm()

   The span parameter controls the decay rate of weights, determining how quickly older data's influence decreases.

2. Step 2: Differentiate from other parameters

   min_periods sets minimum data points for calculation, adjust changes calculation method, and ignore_na handles missing data, none control weight decay speed.

3. Final Answer:

   span -> Option A

4. Quick Check:

   Weight decay speed controlled by span [OK]

Hint: Adjust span to control weight decay speed [OK]

Common Mistakes:

• Confusing span with min_periods
• Using adjust to control weight decay
• Ignoring role of ignore_na