Write a program in Python to caluculate the adjusted and non-adjusted EWM in a given dataframe

The Exponentially Weighted Moving Average (EWM) is a statistical technique that gives more weight to recent observations. Pandas provides two modes: adjusted (default) and non-adjusted, which handle the calculation differently during the initial periods.

Understanding EWM Parameters

The key difference between adjusted and non-adjusted EWM lies in how they handle the bias correction ?

• Adjusted EWM (default): Applies bias correction to account for the initialization period

• Non-adjusted EWM: Uses raw exponential weighting without bias correction

• com parameter: Center of mass, controls the decay rate (higher values = slower decay)

Creating Sample Data

First, let's create a DataFrame with some missing values to demonstrate the EWM calculation ?

import numpy as np
import pandas as pd

df = pd.DataFrame({
    'Id': [1, 2, 3, np.nan, 5],
    'Age': [12, 13, 12, 14, 15]
})

print("Original DataFrame:")
print(df)

Original DataFrame:
    Id  Age
0  1.0   12
1  2.0   13
2  3.0   12
3  NaN   14
4  5.0   15

Calculating Adjusted EWM

The adjusted EWM applies bias correction and is the default behavior ?

import numpy as np
import pandas as pd

df = pd.DataFrame({
    'Id': [1, 2, 3, np.nan, 5],
    'Age': [12, 13, 12, 14, 15]
})

adjusted_ewm = df.ewm(com=0.5).mean()
print("Adjusted EWM:")
print(adjusted_ewm)

Adjusted EWM:
        Id        Age
0  1.000000  12.000000
1  1.750000  12.750000
2  2.615385  12.230769
3  2.615385  13.425000
4  4.670213  14.479339

Calculating Non-Adjusted EWM

The non-adjusted EWM uses raw exponential weighting by setting adjust=False ?

import numpy as np
import pandas as pd

df = pd.DataFrame({
    'Id': [1, 2, 3, np.nan, 5],
    'Age': [12, 13, 12, 14, 15]
})

non_adjusted_ewm = df.ewm(com=0.5, adjust=False).mean()
print("Non-Adjusted EWM:")
print(non_adjusted_ewm)

Non-Adjusted EWM:
        Id        Age
0  1.000000  12.000000
1  1.666667  12.666667
2  2.555556  12.222222
3  2.555556  13.407407
4  4.650794  14.469136

Complete Example

Here's a complete program that calculates both adjusted and non-adjusted EWM ?

import numpy as np
import pandas as pd

# Create sample DataFrame
df = pd.DataFrame({
    'Id': [1, 2, 3, np.nan, 5],
    'Age': [12, 13, 12, 14, 15]
})

print("Original DataFrame:")
print(df)
print("\nAdjusted EWM:")
print(df.ewm(com=0.5).mean())
print("\nNon-Adjusted EWM:")
print(df.ewm(com=0.5, adjust=False).mean())

Original DataFrame:
    Id  Age
0  1.0   12
1  2.0   13
2  3.0   12
3  NaN   14
4  5.0   15

Adjusted EWM:
        Id        Age
0  1.000000  12.000000
1  1.750000  12.750000
2  2.615385  12.230769
3  2.615385  13.425000
4  4.670213  14.479339

Non-Adjusted EWM:
        Id        Age
0  1.000000  12.000000
1  1.666667  12.666667
2  2.555556  12.222222
3  2.555556  13.407407
4  4.650794  14.469136

Key Differences

Conclusion

Adjusted EWM provides bias-corrected exponential smoothing and is the default option. Non-adjusted EWM uses raw exponential weighting, which may be preferred for certain statistical applications where bias correction is not desired.