Window Functions — Rolling, Expanding, EWM

Definition

Window functions compute a statistic over a sliding subset of data. pandas offers three flavors: rolling (fixed-size moving window), expanding (growing window from the start), and ewm (exponentially weighted, recent values weighted more heavily).

graph TD
    A[Window Functions] --> B["rolling(window)
Fixed-size sliding window"]
    A --> C["expanding()
Growing window from start"]
    A --> D["ewm(span/alpha)
Exponentially weighted"]

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.rolling() — Fixed-Size Moving Window

df["sales"].rolling(
    window=7,              # window size (int = row count, or offset string like "7D")
    min_periods=1,           # minimum observations required to produce a value
    center=False,              # whether the window is centered on the current row
    win_type=None                # e.g. "triang", "gaussian" for weighted windows
).mean()

df["sales_7d_avg"] = df["sales"].rolling(7).mean()
df["sales_7d_sum"] = df["sales"].rolling(7).sum()
df["sales_7d_std"] = df["sales"].rolling(7).std()
df["sales_7d_max"] = df["sales"].rolling(7, min_periods=1).max()
 
# Time-based window (requires a DatetimeIndex)
df.rolling("7D").mean()
 
# Custom function
df["sales"].rolling(7).apply(lambda x: x.max() - x.min())

min_periods avoids leading NaNs

With the default min_periods=window, the first window - 1 rows are NaN (not enough data yet). Set min_periods=1 to get a partial-window result from the very first row instead.

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.expanding() — Cumulative/Growing Window

df["sales"].expanding().mean()      # running average from row 0 to current row
df["sales"].expanding().sum()        # equivalent to cumsum()
df["sales"].expanding(min_periods=3).std()

expanding() vs cumulative methods

.expanding().sum() ≈ .cumsum(), and .expanding().max() ≈ .cummax() — expanding is more general because it accepts arbitrary aggregation functions, including custom ones via .apply().

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.ewm() — Exponentially Weighted

df["sales"].ewm(span=7).mean()          # exponential moving average, "span" ~ window size analog
df["sales"].ewm(alpha=0.3).mean()         # direct smoothing factor (0 < alpha <= 1)
df["sales"].ewm(halflife=3).mean()          # weight halves every 3 periods

Parameter	Meaning
span	analogous to a simple moving average’s window size
alpha	smoothing factor directly; higher = more weight on recent data
halflife	periods for the weight to decay by half
com	center of mass, alternate parameterization

EWMA reacts faster to recent changes

Unlike a plain rolling mean where all points in the window are weighted equally, ewm() gives exponentially decreasing weight to older observations — useful for trend-following metrics (e.g. stock price smoothing).

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Combining with GroupBy — Rolling Per Group

df.groupby("city")["sales"].rolling(7).mean()
df.groupby("city")["sales"].transform(lambda x: x.rolling(7).mean())   # keeps original row alignment

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Common Aggregations Available on All Window Types

.mean() / .sum() / .std() / .var() / .min() / .max()
.median() / .count() / .corr(other) / .cov(other)
.apply(custom_func) / .agg([...])

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Related

• 10-DateTime
• 06-GroupBy
• 12-Aggregation-Statistics