Rolling Skewness and Excess Kurtosis from Closing Prices
Summary
This document describes an indicator that estimates skewness and excess kurtosis over a selected rolling period of closing prices. Skewness summarizes distributional asymmetry, while kurtosis describes tail weight relative to a normal distribution. The formulas expand centered third and fourth moments using the rolling mean, then normalize them by powers of the standard deviation; subtracting three from kurtosis produces excess kurtosis. The indicator plots both measures as separate series around a zero reference.
The material explains what the statistics represent and gives an implementation, but it supplies no market examples, empirical tests, or trading rules for interpreting the readings. These are descriptive measures of a chosen sample, so values can shift with the lookback window and may be unstable when observations are limited or prices have unusual behavior. The document also refers to a security's closing-price series without specifying a particular asset or a tested use case.
Key ideas
- Skewness measures asymmetry in a rolling distribution of closing prices.
- Kurtosis describes distributional tail weight, and the formula reports excess kurtosis by subtracting three.
- Both estimates are calculated from rolling moments centered on the rolling mean.
- The indicator presents statistics but does not define trading thresholds or demonstrate predictive value.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.