Rolling Kurtosis Pass Node

Rolling Kurtosis — Series Input

StatisticalDistributionalPass

Overview

The Rolling Kurtosis Pass Node computes excess kurtosis over a rolling window — measuring the "fat-tailedness" of a return distribution relative to a normal distribution.

Excess kurtosis = 0 for a normal distribution. Positive excess kurtosis (leptokurtic) means more extreme outliers than expected; negative (platykurtic) means thinner tails. Financial returns typically show positive excess kurtosis.

Formula

Excess Kurtosis:
kurt[i] = [Σ(xⱼ − μ)⁴ / n] / σ⁴ − 3
μ = rolling mean, σ = rolling standard deviation, computed over window of size n=period.
kurt > 0 = fat tails (leptokurtic). kurt < 0 = thin tails (platykurtic). kurt = 0 = normal (mesokurtic).

Parameters

ParameterDefaultDescription
period20Rolling window in bars

Inputs & Outputs

SlotDirectionTypeDescription
inputInput{ values, timestamps }Any upstream numeric series
valuesOutput(number | null)[]Excess kurtosis per bar; nulls during warm-up
timestampsOutputnumber[]Unix timestamps aligned to input

Use Cases

Tail Risk Detection

Rising kurtosis signals increasing tail risk — consider tightening position sizing or using CVaR-based risk management.

Regime Classification

High kurtosis often accompanies volatile or crisis regimes. Use alongside skewness to classify the current distribution shape.

Options Pricing Context

Fat tails (positive kurtosis) imply options are mispriced by Black-Scholes. Use kurtosis to adjust model inputs or identify mispricings.

Tips & Best Practices

Use Long Enough Windows

Kurtosis estimates are unreliable with small samples. Use period ≥ 30 for meaningful estimates; period ≥ 60 for robust ones.

Combine with Skewness

Kurtosis alone doesn't tell you the direction of the tail risk. Pair with Rolling Skewness Pass to understand whether fat tails lean negative or positive.

Apply to Returns, Not Prices

Feed log-returns or simple returns — not raw prices — into this node. Price-level kurtosis is dominated by trend and scale effects.

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