Rolling standard deviation in Pandas - Step-by-Step Execution

Concept Flow - Rolling standard deviation

Start with data series

↓

Choose window size

↓

For each position in series

↓

Select window slice

↓

Calculate std deviation of slice

↓

Store result

↓

Move window forward

Back to 'For each position'↓

End when series exhausted

↩Back to 'For each position'

The rolling standard deviation slides a fixed-size window over data, calculating the standard deviation for each window slice.

Execution Sample

Pandas

import pandas as pd
s = pd.Series([1, 2, 3, 4, 5])
rolling_std = s.rolling(window=3).std()
print(rolling_std)

Calculate rolling standard deviation with window size 3 on a simple series.

Execution Table

Step	Window slice	Values in window	Std deviation	Output at position
1	positions 0 to 0	[1]	NaN	NaN (window not full)
2	positions 0 to 1	[1, 2]	0.7071	NaN (window not full)
3	positions 0 to 2	[1, 2, 3]	1.0	1.0
4	positions 1 to 3	[2, 3, 4]	1.0	1.0
5	positions 2 to 4	[3, 4, 5]	1.0	1.0
6	End of series	No more windows	N/A	Stop

💡 Reached end of series; no more full windows to compute standard deviation.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	Final
window_slice	None	[1]	[1, 2]	[1, 2, 3]	[2, 3, 4]	[3, 4, 5]	None
std_dev	None	NaN	0.7071	1.0	1.0	1.0	None
output	Empty	NaN	NaN	1.0	1.0	1.0	Series with NaNs and std values

Key Moments - 2 Insights

Why are the first two outputs NaN even though we have data?

Because the window size is 3, the rolling std requires 3 data points to compute. Rows 1 and 2 in the execution_table show the window is not full, so output is NaN.

Why does the standard deviation stay the same (1.0) for the last three windows?

Because the values in each 3-item window increase by 1 consistently, the spread (std deviation) remains constant, as shown in rows 3 to 5 of the execution_table.

Visual Quiz - 3 Questions

Look at the execution_table, what is the output at step 2?

A 0.7071

B 1.0

C NaN

D 0.0

💡 Hint

Check the 'Output at position' column for step 2 in the execution_table.

At which step does the rolling window first produce a valid standard deviation?

A Step 3

B Step 2

C Step 1

D Step 4

💡 Hint

Look for the first non-NaN output in the 'Output at position' column in the execution_table.

If the window size changed to 2, what would be the output at step 2?

A NaN

B 0.7071

C 1.0

D 0.0

💡 Hint

Refer to how window size affects when std deviation starts appearing in the execution_table and variable_tracker.

Concept Snapshot

Rolling standard deviation:
- Use pandas Series.rolling(window).std()
- Window slides over data points
- Std deviation computed only when window full
- Early outputs are NaN if window not full
- Useful for measuring local variability in data

Full Transcript

Rolling standard deviation calculates the standard deviation over a moving window of fixed size on a data series. The window moves one position at a time, and the standard deviation is computed for the values inside the window. If the window is not full (fewer data points than window size), the output is NaN. This method helps understand how data variability changes over time or position. In the example, a window size of 3 is used on a series of 5 numbers. The first two outputs are NaN because the window is not full. From the third position onward, the standard deviation is computed and remains constant because the data increases evenly.