Rolling Windows & Moving Averages

Raw time series are often noisy. Rolling windows smooth that noise and reveal trends by computing a statistic over a sliding window of recent observations. The classic example is a moving average, but the same mechanism powers rolling sums, rolling standard deviations, and expanding (cumulative) statistics.

What You'll Learn

• How to compute a moving average with rolling
• How window size affects smoothing
• How to use min_periods to handle the start of a series
• The difference between rolling and expanding windows

The Moving Average

rolling(window=N) defines a sliding window of N rows. Chaining an aggregation like mean computes that statistic for each window position. This is the standard way to smooth a series.

The first two ma_3 values are NaN because a full 3-row window is not yet available. From the third row onward, each value is the average of the current row and the two before it.

Window Size Controls Smoothing

A larger window smooths more aggressively but reacts more slowly to change. Compare a short and long window on the same series.

The 5-day average is steadier, while the 3-day average follows the data more closely. Choosing the window is a tradeoff between smoothing and responsiveness.

Other Rolling Statistics

rolling is not limited to the mean. You can take a rolling sum, max, min, or standard deviation, which is useful for measuring recent volatility.

min_periods: Values From the Start

By default a window needs to be full before it produces a value. Set min_periods to allow partial windows at the beginning, so you get numbers from the very first row.

The ma_partial column has no leading NaN values because partial windows are allowed.

Expanding Windows

An expanding window grows to include every row seen so far, giving a cumulative statistic rather than a fixed-size one. expanding().mean() is the running average of the whole series up to each point.

Exercise: 3-Day Moving Average

Exercise: Running Total

Key Points

• rolling(window=N).mean() computes a moving average over a sliding window
• Larger windows smooth more but react slower to change
• rolling also supports sum, max, min, and std for recent volatility
• min_periods lets partial windows return values at the start of the series
• expanding grows the window cumulatively for running statistics