Choosing a scale for moving-average oscillators

Unnormalized readings stay in price

A moving average here is a lookback mean of ordered closes. A short mean minus a long mean produces an oscillator. When that oscillator is left as a 4-period versus 8-period spread, it is an unnormalized oscillator: the reading is still a price increment. Its numeric range therefore tracks the instrument, the average price level, and recent volatility. A 0 to 100 indicator does not do that. It stays inside that interval on every series.

Crossings under fixed thresholds

Under fixed theoretical thresholds, both the 4/8 moving-average oscillator and a 5-period 0 to 100 oscillator produced crossings on daily lean-hog futures. On soybean oil the same oscillator thresholds produced no crossings, while the 0 to 100 rules still produced a comparable number.

Four ways to rescale the spread

Four construction choices are specified for rescaling the 4/8 oscillator. Divide it by average price. Divide it by the standard deviation of price. Divide it by average true range of price. Or map the oscillator onto its own historical range.

Average price as a level scale

Average-price construction divides the 4/8 oscillator by an 8-period moving average of closes. The same lookback mean that helps form the spread is reused as a price-level denominator. The output is a fraction of the prevailing price level rather than a raw price increment.

A z-score of closes

Z-score construction divides the 4/8 oscillator by an 8-period population standard deviation of closes. The reading is then in volatility units rather than price increments. With those parameters the scaled values stayed near plus or minus 1 on daily gold futures and on five-minute cocoa futures.

Average true range when closes understate movement

True range equals prior close minus current low when the prior close is above the current high, current high minus prior close when the prior close is below the current low, and high minus low otherwise. Average true range is a moving average of that series. It is used as an alternative volatility denominator when close-to-close dispersion understates intra-bar movement.

In cotton futures from late May through mid-June 1999, eight-period average true range more than doubled relative to eight-period close-to-close standard deviation. Dividing the oscillator by average true range damped that window more than dividing it by standard deviation.

A Williams %R map of the oscillator

Williams %R construction sets the output to 100 times (value minus lookback minimum) divided by (lookback maximum minus lookback minimum). The reading is limited to 0 to 100 regardless of instrument, timeframe, or input scale. The same map can be applied to price or to an already computed oscillator.

Applying that range map to the raw 4/8 oscillator with a 200-bar lookback produced a weekly S&P 500 series whose numeric range stayed more consistent across changing price and volatility levels. It was the only examined form that hard-caps output at 0 and 100.

What the scalings are for

After these scalings, indicator values are described as more consistent for long-history comparison, cross-instrument comparison, and multi-timeframe comparison. They are also described as less dominated by sudden volatility changes.