Constructing excess and momentum difference-curve oscillators

What a difference-curve records

Difference-curve oscillators are built by choosing two quantities and plotting their daily difference as a line that can sit under a price bar chart for comparison. The difference-curve is that daily series: one specified quantity minus the other, with the plotted values connected as a line.

Moving-average spans inside an oscillator are meant to match the intended holding horizon. A short-horizon rule is not to be built from momentum of a 200-day average.

A relative-price-excess construction

Relative-price-excess is the gap between price and a moving average, used to mark closes that sit unusually far above or below that average relative to their usual relationship. One construction subtracts a 24-day simple moving average from the close, so the oscillator crosses zero as price fluctuates through that average.

Extremes on that excess oscillator mark closes farther above or below the average than usual, under the assumption that a later recross of the average requires the move that produced the extreme to slow or reverse.

Wait for a confirmation-average cross

A confirmation-average is a moving average of the oscillator itself, used so a rule waits for a cross instead of acting at an unconfirmed peak or trough. A 12-day average of the excess oscillator can delay action until the oscillator crosses that average, accepting later recognition of turns in exchange for fewer unconfirmed reversals.

A smoother excess oscillator

Replacing the raw close with a 6-day exponential average of the close, then subtracting the 24-day simple average, produces a smoother excess oscillator that omits many lesser signals.

A momentum-oscillator from a lookback-offset-pair

A momentum-oscillator is a difference between a moving average and the same average a fixed number of observations earlier, used to watch whether the average’s change is speeding up or slowing. It is constructed by subtracting from a moving average its value a fixed number of days earlier. One specification is a 12-day simple average minus its value four days prior.

That pair is the lookback-offset-pair: the moving-average length together with the lag used to difference that average against its own earlier value. The momentum series is above zero while the average is rising and below while it is falling, and the series itself rises or falls as the average’s change accelerates or slows.

Keep the offset as short as the chart still allows

Each momentum reading corresponds to a point on the average about half the offset earlier, so a four-day offset reflects the average from about two days before. The offset is to be kept as short as still yields a readable chart, including a one-day offset on a 12-day average.

The same construction on a longer pair

Switching the same momentum construction to a 30-day average with a 10-day offset keeps some signals from the 12-day, four-day pair while dropping shorter-term turns associated with the shorter base.