Constructing a probability-defined trend filter

Trend as a signal-to-noise ratio

Trend can be constructed as a signal-to-noise ratio in which directional price movement is the signal and random movement is the noise.

Common momentum trend indicators are similar ratios of a momentum term to a noise term and therefore tend to be highly correlated and to display lag from averaging and smoothing.

New highs and new lows as Bernoulli trials

An alternative construction estimates new-high and new-low probabilities by treating each period's break of the prior period high or low as a Bernoulli trial, with a large-sample no-trend expectation near 0.5.

The probability series is built by coding 1 or 0 for a new high and a new low each period, including both events on an outside day and neither on an inside day, then averaging the binary series over a chosen lookback such as 25 periods.

A bounded trend-strength measure

The difference between new-high probability and new-low probability can be used as a bounded trend-strength measure, with idealized values of 1.0, -1.0, and 0 for a perfect uptrend, perfect downtrend, and no trend.

Editorial reading of the construction

Editorial interpretation: Once the lookback is chosen and each period is coded for a new high and a new low, the no-trend expectation near 0.5 and the sign of the probability difference become an explicit hypothesis about the chart. That statement is a construction choice, not a claim about later market results.