Reverse-engineered Relative Strength Index price curves

What the reverse-engineered curves plot

RevEngEMARSI and RevEngSMARSI are constructed so that today's plotted value is the next bar's close that would make a k-period Relative Strength Index touch its n-period exponential or simple moving average.

AUC and ADC in the inversion

AUC and ADC are the (2k-1)-period exponential moving averages of up-close and down-close increments, and they enter the algebraic inversion that produces the reverse-engineered price curves.

Daily and weekly next-bar closes

On a daily chart the current RevEngEMARSI reading is the close needed tomorrow for tomorrow's k-period Relative Strength Index to meet its n-period exponential moving average. On a weekly chart the same construction applies to the next week.

Weekly Nikkei 225 example

In the weekly Nikkei 225 example, a 14-period Relative Strength Index and a 65-period exponential moving average of that Relative Strength Index are mapped onto price via RevEngEMARSI so each week's value is the next week's close that would push the Relative Strength Index onto that exponential moving average.

For the week dated 10 February 1994 the index closed at 19990 while RevEngEMARSI stood at 18913, stating the next-week close that would force the 14-period Relative Strength Index onto its 65-period exponential moving average.

The following week closed at 18960 with the Relative Strength Index at 49.62 versus an exponential moving average of 49.35, so the price-space projection sat near the later close because the Relative Strength Index approached but did not land exactly on the exponential moving average.

Reverse-engineered trendline levels

RevEngTrendRSI is built by writing the Relative Strength Index trendline as a function of elapsed bars between two dated Relative Strength Index points, then inverting that next-bar trendline level through the same AUC and ADC construction used for the moving-average versions.

On weekly DJIA, the Relative Strength Index trendline between 12 October 1990 and 9 October 1992 spans 104 trading weeks with Relative Strength Index values 32.9383 and 36.8033, and RevEngTrendRSI maps that line's support-resistance role onto price.

When chart scale changes

A drawn Relative Strength Index trendline and a coded trendline indicator coincide on an arithmetic monthly Relative Strength Index chart, but the same drawn line shifts relative to the Relative Strength Index on a semilog monthly chart, so the formula must be adjusted when scale changes.