Constructing a cycle-free trend filter against an ATR-scaled random walk

A cycle-free filter

Many conventional indicators depend on staying synchronized with changing cyclic market content, and become out of phase when that alignment is lost.

A trend filter can be constructed to identify direction without first locating the market inside a cycle. That design is a cycle-free filter: direction is read from realized travel, not from a prior cycle location.

The random-walk baseline

Under a simple random-walk model, expected net displacement after n steps equals the square root of n times average step length. That expectation is the random-walk baseline.

Up-walk and down-walk readings

An up-walk reading equals the current high minus the lowest price of the last n periods, divided by k times average true range over those k periods, where k is the count from that low to the present.

A down-walk reading uses the same structure with the lookback high and the current low, then the same k-times-ATR scale.

Why the denominator uses ATR-scaling

Scaling both walks by k times average true range is intended to make them comparable to a random walk and to walks computed on other price series. That placement of average true range is ATR-scaling.

Without that time-and-volatility denominator, walk readings from dissimilar markets would not be directly comparable.

The unit-trend-threshold

A walk series above 1 was treated as indicating a trend in that direction. That cutoff is the unit-trend-threshold.