Constructing nested stochastic lookbacks

A stack of nested clocks

The archive built a nested-lookback-stack: the same stochastic formula computed at several horizons and drawn together so short, intermediate, and long sampling windows can be compared. Several stochastic lengths were observed to reach an extreme reading at the same time, which motivated overlaying those series on one chart.

Editorial: read that overlay as a stack of nested clocks. Choose several lookbacks, keep one smoothing convention, and share the same extreme-band levels, then study only the moments those clocks agree. Lookback design is the lesson, not a search for one default length.

Calendar-matched lookbacks

A 14-bar monthly stochastic, a 59-bar weekly stochastic, and a 294-bar daily stochastic were treated as comparable lookbacks because 59 weeks and about 294 trading days each span about 14 months.

Editorial: those three series are different sampling clocks aimed at roughly the same span. Comparability comes from matching the window, not from forcing every chart to use one bar length.

Unoptimized pairs and simple-average-smoothing

Four unoptimized parameter pairs were assigned to long, intermediate, short, and very-short horizons: 150/5, 50/5, 13/5, and 5/5. Each pair states the percent-k lookback and the percent-d smoothing length.

The overlaid series were calculated with simple moving averages rather than exponential averages. That choice is simple-average-smoothing. Percent-d is a smoothed transform of percent-k, formed here with a simple moving average of a stated length.

How percent-k and percent-d were stated

Percent-k locates the latest close inside the highest high and lowest low of a chosen lookback, scaled from 0 to 100. In the archive statement, percent-k is 100 times the latest close minus the n-period lowest low, divided by the n-period high-low range. A three-period percent-d was formed from the summed numerators and denominators of that ratio.

Shared extreme bands and a short trigger

An extreme-band is a fixed threshold, here 80 or 20, used to mark when a series is stretched inside its own lookback range. On the illustrated daily index overlay of 150/5, 50/5, and 13/5, concurrence above 80 or below 20 was the condition of interest, and the 13/5 series crossing those bands was used as the trigger.

The longer-window-gate

A longer-window-gate accepts a shorter-length band cross only when a longer-length series is already beyond the same band. An intermediate-horizon rule accepted a 50/5 cross of 80 or 20 only if the next-longer 150/5 series was already above 80 or below 20, respectively. A 50/5 cross of the 20 line was rejected as a buy condition when the 150/5 series had not yet fallen below 20.

An oscillator, not a full-run companion

The construction was described as an oscillator rather than a trend-following rule, so it would not stay with an entire directional run. Daily screening for a specified multi-length stochastic pattern typically selected fewer than 1 percent of names in the database, and on some days selected none.

Editorial: asking several clocks to agree, then applying a longer-window-gate, is a construction that stays quiet most days. The archive recorded that sparsity as a property of the overlay, not as a performance result.