Pandas Window Functions (rolling / expanding / ewm)

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Window functions are used for sliding-window calculations on time series or ordered data, and are essential tools in fields such as financial analysis and signal processing.

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rolling: Sliding Window

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Basic Usage

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Example

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import pandas as pd\n\nimport numpy as np\n\n# Create time series data\n\nnp.random.seed(42)\n\ndates = pd.date_range("2024-01-01", periods=20, freq="D")\n\nts = pd.Series(np.random.randint(100,200,20), index=dates)\n\nprint("Original data (first 10 rows):")\n\nprint(ts.head(10))\n\nprint()\n\n# 7-day rolling average\n\nma7 = ts.rolling(window=7).mean()\n\nprint("7-day rolling average (first 10 rows):")\n\nprint(ma7.head(10))\n\nprint()\n\n# Rolling sum\n\nrolling_sum = ts.rolling(window=5).sum()\n\nprint("5-day rolling sum:")\n\nprint(rolling_sum.head(10))\n

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Sliding Window Types

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Example

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import pandas as pd\n\nimport numpy as np\n\ns = pd.Series([1,2,3,4,5,6,7,8,9,10])\n\n# Fixed window size\n\nprint("Fixed window (3):")\n\nprint(s.rolling(3).mean())\n\nprint()\n\n# Moving window (time-based window)\n\n# 1-minute window\n\ns2 = pd.Series([1,2,3,4,5], index=pd.date_range("2024-01-01", periods=5, freq="T"))\n\nprint("Time-based window (1 minute):")\n\nprint(s2.rolling("1min").sum())\n

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expanding: Expanding Window

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The expanding window accumulates from the start up to the current position, gradually increasing in size.

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Example

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import pandas as pd\n\nimport numpy as np\n\ns = pd.Series([1,2,3,4,5])\n\n# Expanding window: cumulative mean\n\nexp_mean = s.expanding().mean()\n\nprint("Cumulative mean:")\n\nprint(exp_mean)\n\nprint()\n\n# Expanding window: cumulative maximum\n\nexp_max = s.expanding().max()\n\nprint("Cumulative maximum:")\n\nprint(exp_max)\n\nprint()\n\n# Expanding window: cumulative standard deviation\n\nexp_std = s.expanding().std()\n\nprint("Cumulative standard deviation:")\n\nprint(exp_std)\n

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ewm: Exponentially Weighted Moving Average

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Exponentially Weighted Moving Average (EWMA) assigns greater weight to more recent data points.

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Example

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import pandas as pd\n\nimport numpy as np\n\ns = pd.Series([1,2,3,4,5,6,7,8,9,10])\n\n# Smaller alpha gives higher weight to recent data\n\newm_05 = s.ewm(alpha=0.5).mean()\n\newm_2 = s.ewm(alpha=0.2).mean()\n\nprint("Original data:")\n\nprint(s.values)\n\nprint("nalpha=0.5:")\n\nprint(ewm_05.values)\n\nprint("nalpha=0.2:")\n\nprint(ewm_2.values)\n\nprint()\n\n# Using span (relation to alpha: alpha = 2/(span+1))\n\newm_span = s.ewm(span=5).mean()\n\nprint("span=5:")\n\nprint(ewm_span.values)\n

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EWM is more sensitive to trend changes and suitable for scenarios requiring rapid response.

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Practical Application: Stock Technical Indicators

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Example

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import pandas as pd\n\nimport numpy as np\n\n# Simulate stock price data\n\nnp.random.seed(42)\n\ndates = pd.date_range("2024-01-01", periods=30, freq="D")\n\ndf = pd.DataFrame({\n\n"Date": dates,\n\n"Closing Price": 100 + np.random.randn(30).cumsum()\n\n})\n\n# Compute technical indicators\n\n# 5-day moving average\n\ndf= df.rolling(5).mean()\n\n# 10-day moving average\n\ndf= df.rolling(10).mean()\n\n# 5-day exponential moving average\n\ndf= df.ewm(span=5).mean()\n\n# Volatility (5-day rolling standard deviation)\n\ndf= df.rolling(5).std()\n\n# Cumulative highest price\n\ndf= df.expanding().max()\n\nprint("Stock technical indicators:")\n\nprint(df.round(2))\n

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Comparison of Window Functions

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Type	Description	Applicable Scenarios
rolling	Fixed-size window	Moving averages, volatility
expanding	Cumulative window	Cumulative statistics, stop-loss/take-profit
ewm	Exponentially weighted	Trend tracking, rapid response