Rebuilding rate of change as a path-weighted oscillator

Ordinary rate of change

Ordinary rate of change is defined as current price minus the price from T periods earlier, divided by that lagged price and scaled by 100. Other common two-price ratios of the same pair are treated as algebraically equivalent.

The result is a momentum reading formed from the relative change between the current price and a price lagged a stated number of periods. The familiar percentage-change scale is kept. What changes is whether the window is allowed to ignore everything between its two endpoints.

The two-point problem

Ordinary rate of change uses only the current bar and the bar T periods earlier, so observations between those two dates do not enter the reading. Separate price paths that begin and end at the same two prices therefore receive the same ordinary rate-of-change value even when the intervening trajectories differ.

The construction has no inherent smoothing, unlike constructions that average or sum many observations, so isolated noise in the two endpoint prices passes straight into the oscillator. A single isolated price change also moves the ordinary series twice: once when the change enters the lookback and again T bars later when that same change drops out.

Adjusted rate of change

The adjusted rate of change computes every one-step rate of change between the original endpoints, applies exponential smoothing with a lookback equal to that span, and multiplies the smoothed series by the same span so the result stays on a comparable scale.

Exponential smoothing is a recursively weighted average over a defined lookback that gives more influence to recent observations than to older ones. Because those weights favor recent one-step changes, the delayed second peak or trough that appears T bars after a one-bar jump is removed from the adjusted series.

When three paths share one ordinary reading

In a three-path example that shared one ordinary reading, the adjusted values at the final bar were 0.62 on the lowest path, 0.27 on the middle path, and -0.09 on the uppermost path. Those prints match the intended ranking that the lowest path should score highest.

Divergence and historically extreme prints

The adjusted series is applied to the same chart tasks as ordinary rate of change, including price-indicator divergence and comparison of trend breaks. Divergence is a chart condition in which price and a momentum series fail to confirm each other, used as a candidate reversal hypothesis rather than a completed forecast.

A worked chart used a 21-period adjusted series to mark a divergence that the unadjusted series did not show. Neither the ordinary nor the adjusted form is given fixed overbought or oversold bands. Historically extreme prints are treated only as a cue to inspect for a possible turn.