rolling mean vs cumulative mean

The rolling mean and cumulative mean are both methods for smoothing or summarising data over time, but they differ in scope and window size.

Rolling Mean (Moving Average)

• Definition: The rolling mean calculates the average of a fixed-size window that moves across the dataset.

• Purpose: Captures local trends and smooths short-term fluctuations.

• Example:

  Data: [2, 4, 6, 8, 10]
  Window = 3
  Rolling mean = [NaN, NaN, 4, 6, 8]
  

  (Each value is the mean of the previous 3 observations.)

• Use Cases:

  • Smoothing noisy data.
  • Detecting local trends or seasonal effects.
  • Feature creation in time series models.

Cumulative Mean (Expanding Mean)

• Definition: The cumulative mean computes the average from the start of the dataset up to the current point.

• Purpose: Shows the long-term average as more data becomes available.

• Example:

  Data: [2, 4, 6, 8, 10]
  Cumulative mean = [2, 3, 4, 5, 6]
  

  (Each value is the mean of all previous observations up to that point.)

Use Cases:

• Monitoring convergence of a process.
• Observing long-term stability.
• Evaluating cumulative performance metrics.

Comparison Summary

Feature	Rolling Mean	Cumulative Mean
Window Size	Fixed (e.g., last 7 days)	Expanding (start → current)
Focus	Local trends	Global, long-term trend
Sensitivity	Reacts to short-term changes	Smoothed by all past values
Example Tool	Series.rolling(window).mean()	Series.expanding().mean()