2003issue C081-16
Reverse-engineered RSI price targets
A smoothed relative strength index can be inverted so a chart plots the next-bar price that would keep the oscillator on a chosen exponential or simple path. This article reconstructs that inverse for both smoothers, including the piecewise mapping from the recovered increment back to price.
- The construction recovers a next-bar price that would produce a chosen exponential or simple moving average of the relative strength index.
- Wilder-period exponential smoothing is applied to one-bar up-moves and down-moves, then RSI is smoothed again over a longer window before inversion.
- If the inverted increment is non-negative, the plotted price is the close plus that increment; otherwise the increment is scaled by the complementary RSI ratio.
- The simple-mean variant replaces the exponential RSI smoother and uses a one-bar-shorter average window, while a trendline inversion is treated as specified elsewhere.
What the inverse recovers
The relative strength index is a bounded oscillator built from averaged up-closes and down-closes over a lookback. In this construction it is the quantity being inverted rather than a standalone signal.
The construction recovers a next-bar price that would produce a chosen exponential or simple moving average of that oscillator. Exponential smoothing is a recursively weighted average applied both to the RSI series and to the up-move and down-move streams that feed Wilder's formulation. A moving average, used in parallel, is an unweighted lookback mean of RSI values inverted to recover a matching next-bar price.
Exponential reverse-engineered RSI
The exponential variant first computes RSI with a 14-bar Wilder period. Average up-change and average down-change are themselves exponentially smoothed over the same Wilder period from one-bar positive and negative close-to-close moves.
After that oscillator is formed, RSI is exponentially averaged over a 45-bar window. That second smoother is the path the inverse is asked to hold.
From increment to next-bar price
The inverted increment X is the Wilder period minus one, times the quantity given by average down-change times smoothed RSI over 100 minus smoothed RSI, minus average up-change.
When X is non-negative the plotted price is close plus X. Otherwise it is close plus X times 100 minus smoothed RSI, over smoothed RSI.
Simple mean and other presentations
The simple-average variant substitutes a 45-bar simple mean of RSI, using a one-bar-shorter average window, for the exponential RSI smoother. It keeps the same inversion algebra.
Equivalent exponential and simple reverse-engineered RSI formulas appear in other package languages with the same 14 and 45 default parameters and the same piecewise close-plus-X mapping.
A third related construction inverts an RSI trendline rather than a moving average of RSI. That variant is treated as already specified elsewhere.
All readings on this track · 41 readings
- 1984Matching average age across price filters
- 1984Residual-impact construction of exponential smoothers
- 1988Constructing simple and exponential moving averages as specified filters
- 1989Evaluating smoothed free reserves and funds-discount spreads
- 1990Integer construction of moving averages and exponential smoothing
- 1990Constructing incremental moving average filters
- 1991Constructing a double-smoothed stochastic oscillator
- 1991Constructing an exponential average from a smoothing weight
- 1991Constructing a double-smoothed momentum oscillator family
- 1991Competing certainty rules from exponential-average conditions
- 1991Hybrid construction of a mechanical timing system from smoothed signals
- 1991Constructing an exponential smoother from a moving-average length
- 1991Equivalent relative-strength-index constructions from a ratio and from smoothed momentum
- 1991Constructing the true strength index from double-smoothed momentum
- 1991True strength index from signed, double-smoothed momentum
- 1992Constructing exponential averages from simple lookbacks
- 1992Constructing exponential averages by the smoothing constant, startup length and lag
- 1992Nested range smoothing and windowed high-low damping
- 1992A weekly equity stance from the discount-bill spread
- 1993Double-smoothed stochastics momentum index construction
- 1993Constructing the true strength index with double exponential smoothing
- 1994Polarized fractal efficiency with a shared exponential smoother
- 1994Five-interval exponential smoothing of ten-interval signed path-efficiency
- 1994Hand-ranked price-volume series with stacked smoothing and stochastic
- 1995Range expansion filter on multi-horizon averages
- 1995The exponential smoothing constant from averaging lag
- 1997Construct a nested-average rainbow band and oscillator
- 1998Filter stacks that combine a moving average with exponential smoothing
- 2002Smoothed relative-strength construction from wilder-averaging and a price prefilter
- 2003Reverse-engineered RSI price targets
- 2004Piecewise trend quality from moving-average reversals
- 2004Nested smoothing recipes versus unaudited oscillator experiments
- 2008Weight construction beyond the N-day label
- 2010A consensus filter for objective RSI and smoothing construction
- 2012Sentiment-zone oscillator from signed closes
- 2012Classic RSI one-over-N smoothing versus the standard exponential average
- 2013Why exponential smoothing uses two over n plus one
- 2015Constructing ratio indicators with moving-average and exponential-smoothing weights
- 2015Slow relative-strength index from an exponentially smoothed price
- 2017Rebuilding the relative strength index as open-scale buy-sell pressure
- 2017Comparing Wilder and exponential smoothing inside a relative-strength index