How do rolling and expanding window functions work in Pandas?

Window functions compute statistics over a sliding or expanding subset of rows, essential for time-series smoothing, trend detection, and feature engineering. Unlike groupby aggregations, window functions return a result for every row, preserving the original index.

import pandas as pd
import numpy as np

ts = pd.DataFrame({
    'date':  pd.date_range('2024-01-01', periods=10, freq='D'),
    'sales': [100, 120, 90, 150, 200, 130, 110, 180, 160, 140],
})
ts = ts.set_index('date')

# --- Rolling window (fixed-size, slides one step at a time) ---
ts['ma3']   = ts['sales'].rolling(window=3).mean()  # 3-day moving avg
ts['std3']  = ts['sales'].rolling(window=3).std()
ts['min3']  = ts['sales'].rolling(window=3).min()

# First window-1 values are NaN (not enough history)
# min_periods: require fewer observations before computing
ts['ma3_mp'] = ts['sales'].rolling(window=3, min_periods=1).mean()

# --- Expanding window (grows to include all rows so far) ---
ts['cum_max']  = ts['sales'].expanding().max()
ts['cum_mean'] = ts['sales'].expanding().mean()

# --- Exponentially weighted moving average (more weight on recent data) ---
ts['ewma'] = ts['sales'].ewm(span=3).mean()

# --- Lag / shift features (common in time-series forecasting) ---
ts['lag1'] = ts['sales'].shift(1)   # yesterday's sales
ts['lag7'] = ts['sales'].shift(7)   # last week's sales
ts['pct_change'] = ts['sales'].pct_change()  # % change from previous row

Moving averages (rolling mean) smooth out noise to reveal trends. Exponentially weighted moving averages give more influence to recent observations, making them responsive to recent changes while still smoothing. Lag features turn a time-series prediction problem into a supervised learning problem where past values predict future ones.

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