Kurtosis

Windowed · default period 20Statistics

The Kurtosis node computes excess kurtosis (Fisher's definition: population kurtosis − 3) over the rolling window. Zero means a normally-shaped distribution (mesokurtic); positive values indicate fat tails (leptokurtic — more extreme events); negative values indicate thin tails (platykurtic). Fat-tailed return distributions are a direct warning for tail-risk events and option mispricing. Requires at least 4 non-null values.

Algorithm

  • Compute mean (μ) and population std (σ) of non-null window values
  • excess kurtosis = (Σ ((x − μ) / σ)⁴ / n) − 3
  • Returns 0 when σ = 0 (constant series)
  • Requires ≥ 4 non-null values; returns null otherwise

Parameters

NameTypeDefaultDescription
periodnumber20Rolling window size. Minimum 4.

Inputs & Outputs

PortTypeDescription
Inputs
inputnumber[]Source numeric array
Outputs
valuesnumber | nullComputed value at each bar; null before the warmup period completes
timestampsnumber[]Bar timestamps (UNIX ms), aligned 1-to-1 with values
Live mode: In live streaming mode the node updates only the last bar in-place rather than recalculating the full array, keeping CPU usage minimal during real-time data feeds.

Use Cases

Tail Risk Alert

Kurtosis exceeding 3 on a return series indicates the distribution has fat tails — increase position-size conservatism or widen stops during such regimes.

Options Strategy Filter

High kurtosis periods favor long-gamma strategies (strangles/straddles); low kurtosis favors short-gamma approaches, guiding vol strategy selection.

Distribution Quality Monitor

Monitor kurtosis on an indicator series to detect whether its distribution has shifted meaningfully, which can invalidate fixed thresholds calibrated on historical data.