Percentile

The Percentile module computes a conditional quantile for each data point in a series. For every value, it filters the entire dataset to include only values less than or equal to the current value, then calculates the specified percentile of that filtered subset.

$$\text{Output}_i = Q_p\bigl(\{x \in \text{Data} \mid x \leq \text{Data}_i\}\bigr)$$

Where $Q_p$ represents the $p$-th quantile (with $p$ specified by the Percentile parameter from 1 to 100).

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How It Works

flowchart TD
    subgraph Input["Input Data"]
        D["Data: [10, 25, 15, 30, 20]"]
        P["Percentile: 50"]
    end
    
    subgraph Process["For Each Value"]
        V["Current value = 25"]
        F["Filter: values ≤ 25<br/>[10, 25, 15, 20]"]
        Q["Compute 50th percentile<br/>of filtered set"]
    end
    
    subgraph Output["Result"]
        R["Output = 17.5"]
    end
    
    D --> V
    P --> Q
    V --> F --> Q --> R

Step-by-step for a single data point:

1. Take the current value (e.g., 25)
2. Filter the entire dataset to values ≤ 25: [10, 25, 15, 20]
3. Compute the specified percentile (e.g., 50th) of that filtered subset
4. Result: 17.5 (the median of [10, 15, 20, 25])

This process repeats for every data point in the series.

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Understanding the Percentile Parameter

The Percentile parameter (1–100) specifies which quantile to compute on the filtered subset:

Percentile	Meaning
25	First quartile of values ≤ current
50	Median of values ≤ current
75	Third quartile of values ≤ current
100	Maximum of values ≤ current (equals current value)

⚠️ Important: This is not a percentile ranking (how the current value ranks relative to history). Instead, it computes a quantile of a dynamically filtered dataset.

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Practical Applications

1. Dynamic Support Level Detection

When the percentile parameter is set low (e.g., 25), the output approximates dynamic support levels—the lower quartile of all values that don't exceed the current price:

flowchart LR
    subgraph Concept["Support Level Logic"]
        Price["Current Price"]
        Filter["Values ≤ Price"]
        Q25["25th Percentile"]
        Support["Dynamic Support"]
    end
    
    Price --> Filter --> Q25 --> Support

2. Distribution Analysis

By comparing outputs at different percentile settings:

Setting	Interpretation
PERC(25) vs PERC(75)	Spread of lower values indicates distribution skew
PERC(50)	Central tendency of filtered distribution
PERC(100)	Always equals the input (identity transformation)

3. Conditional Median Tracking

Using PERC(50) gives you the median of all values up to and including each point—useful for understanding how the "typical" value evolves relative to each observation:

flowchart TD
    subgraph Strategy["Conditional Median Strategy"]
        Data["Price Series"]
        PERC50["PERC(50)"]
        Compare{"Price > PERC(50)?"}
        Above["Above conditional median<br/>Relative strength"]
        Below["At or below<br/>conditional median"]
    end
    
    Data --> PERC50 --> Compare
    Compare -->|Yes| Above
    Compare -->|No| Below

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Example Walkthrough

Consider data series: [100, 80, 120, 90, 110] with Percentile = 50

Index	Current Value	Filtered Set (≤ current)	50th Percentile	Output
0	100	[100, 80, 90]	90	90.0
1	80	[80]	80	80.0
2	120	[100, 80, 120, 90, 110]	100	100.0
3	90	[80, 90]	85	85.0
4	110	[100, 80, 90, 110]	95	95.0

Note: The filter considers the entire dataset, not just preceding values.

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Key Characteristics

Whole-series analysis: The filter examines all data points, not a rolling window. Each output depends on the entire input series.

Non-monotonic relationship: Higher input values don't necessarily produce higher outputs—it depends on the distribution of the filtered subset.

Boundary behavior:

• At Percentile = 100, output always equals input (maximum of set ≤ value is the value itself)
• At Percentile = 1, output approaches the minimum value in the dataset for most inputs

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Advantages

• Context-aware — Output reflects distribution characteristics relative to each observation
• Flexible — Different percentile settings reveal different aspects of the data
• Non-parametric — No distributional assumptions required

Limitations

• Non-intuitive — The conditional filtering logic differs from standard percentile ranking
• Non-causal by design — see Non-Causality below
• Sensitive to outliers — Extreme values affect filtered subset compositions

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Non-Causality

This module is not a running/rolling percentile. Every output is computed against the full analyzed series, including bars that occur after it — a historical value's output can change if later data changes the filtered subset. Historical outputs are ranked against later data and are not tradeable signals; only the newest bar's output (live, or the last bar of a backfill) is causal, because at that point there is no later data left to influence it. Do not backtest a strategy that reacts to a historical PERC value expecting it to reproduce what was knowable at that time — build a causal running-percentile module for that use case instead.

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Missing Data

A missing (null) value in the data series is excluded from every reference sample it would otherwise fall into — it never fabricates a zero or a carried-forward value. A missing pivot itself produces a null output at that position; every other position's calculation is unaffected. Live execution returns exactly one datapoint (the newest bar), null when that bar's value is missing.

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Further Reading

• Quantile - Wikipedia
• Order Statistics
• Conditional Distribution