Price-rooted lookbacks for a relative strength index, a moving average, and a trend filter

One shared clock from the traded level

The construction starts with the traded level. Successive square roots of that market price are taken until four values exist. Those four values are the nested-square-root ladder, and they are treated as a complete set of period candidates for lookback lengths on common indicators.

A relative strength index, a moving average, and a trend filter can then use that same ladder. The relative strength index is a momentum oscillator whose lookback can be taken from a nested square-root of the traded level instead of a conventional fixed count. The moving average is a smoother whose averaging window can be taken from the same nested-root ladder as the other filters in the set. The trend filter is a directional gate whose confirmation length can share that same price-derived period set.

Reading the nested-square-root ladder

Each integer window assigned from one of the nested roots is a lookback periodicity for an indicator.

A price near 17000 produces rounded nested roots of 130, 11, 3, and 2. A price near 1600 produces rounded nested roots of 40, 6, 3, and 2.

Choosing the operative series

The operative series is the price or first-root series the indicators actually measure once the level sits above or below the stated thresholds.

When the price is above 1526, the first square root can become the series the indicators act on, and the remaining roots become its periods.

At a whole-number price of 1600 or lower, the fourth nested root rounds to the same integer as the third. Below that 1600 threshold, the third nested root can be used twice, or the raw price can be used with the first three roots.

Smoothing the look of the indicators

Taking periods from the price itself is presented as a way to smooth how volatile the indicators look.