Estimating a Uniformity Factor for Price-Change Scaling

Summary

The document describes an indicator for testing how price changes scale with the number of bars in a window. It calculates average price changes across sliding windows, dividing by the window length raised to an exponent F. It searches values from 0.1 to 1.0 and selects the factor that makes the resulting statistics most uniform, using minimum variance, a mean-median-mode discrepancy, or the Gini coefficient. A factor of 1 corresponds to ordinary averaging; values near one-half are presented as typical outcomes.

The proposed uses include scaling inputs for machine-learning models, choosing sampling lengths for volatility analysis, and flagging symbols or timeframes with unusual scaling behavior. The document provides a sample table for a silver time series and says chart examples show results across daily, hourly, and minute intervals. It does not establish that the method improves forecasts or trading performance. The factor is estimated from available historical bars, so it may depend on the sample, market, timeframe, and chosen uniformity measure; the random-walk framing is a hypothesis to examine, not a demonstrated property of prices.

Key ideas

• The indicator scales average price changes by the number of bars raised to an exponent.
• It selects an exponent by minimizing a measure of dispersion or distributional irregularity.
• The proposed uniformity measures are variance, a mean-median-mode error, and the Gini coefficient.
• The estimated factor may help normalize model inputs or compare price behavior across symbols and timeframes.
• A fitted factor describes the sample and does not by itself validate a forecasting or trading edge.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.