Constructing breadth, RSI, and stochastic range filters

A shared rescale-and-compare checklist

TradersWeek editorial: Filter construction can be read as one checklist rather than three unrelated studies. Name the raw series, lock the lookback-window, map the series into that window, then park the result on the same chart as price so the reading can be audited before it is treated as a signal.

The named series in this workflow are a market-breadth composite, a relative strength index of the close, or the bin densities of a price-distribution function. A stochastic oscillator is the shared range-rescale: each series is placed inside its recent highest and lowest values before comparison.

Collect the market-breadth workspace

A market-breadth workspace starts by collecting an index, advancing issues, declining issues, new highs, and new lows, then building a composite that subtracts declines from advances. That constructed composite of advancing versus declining issues, new highs, and new lows is the raw input to a range-rescaled filter.

Build the centered breadth filters

Advance-decline relative strength is constructed by centering a 5-bar highest-lowest rescale of the cumulative breadth composite and subtracting the same 5-bar rescale of the companion close.

New-high strength and new-low strength apply that same centered range-rescale to the new-high and new-low series, using lookbacks of 4 bars and 8 bars respectively. Those readings are new-high and new-low strength, each with its own lookback-window.

Place the breadth filters on one chart

The finished breadth filters can be overlaid on a single index chart and, when the source bars are daily, compressed together to a weekly sampling interval.

Documented horizontal references for those constructed series are -30 on advance-decline relative strength, 30 on new-low strength, and -40 together with 40 on new-high strength.

Rescale relative strength index

A stochastic relative-strength-index reading is built by computing a 14-period RSI of the close, locating the 14-period high and low of that RSI, and dividing the distance from the low by that RSI range. Relative strength index is a bounded reading of ordered closes over a stated lookback, used both as a standalone study and as the inner series of that stochastic transform.

Report price-bin density

A price-distribution function reports the share of closes that fall in one interval of a lookback high-low range. One stated parameterization uses interval 6, a 50-bar lookback, and 10 intervals.

A 10-interval, 50-bar report can compute each bin share, the peak share, the modal interval and price, the current close's bin, and a mobility oscillator from the gap between current-bin density and peak density.

Form the mobility oscillator

The same histogram-and-mobility construction can be run with a 14-bar lookback and 10 intervals, then optionally smoothed with a 7-bar average of the mobility reading.

The mobility oscillator takes interval count and lookback as inputs, defaults in one implementation to 10 intervals and 14 bars, signs the reading when the close is below the modal price, and can be called from a rule set for historical testing.