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2003issue C061-7

Reverse-engineered RSI as a next-close projection

For a k-period Relative Strength Index, one-day closing prices and the corresponding RSI values stand in one-to-one correspondence, so a hypothesized next RSI uniquely determines the next close. That inverted reading is the RevEngRSI.

  • For a k-period RSI, one-day closing prices and the corresponding RSI values are in one-to-one correspondence, so a hypothesized next RSI uniquely determines the next close.
  • If the hypothesized next RSI is above today's RSI, the implied next close is above today's close; if it is below, the implied next close is below today's close.
  • After an RSI support, resistance, or projected future RSI is identified, a RevEngRSI series for that value states the next close at which RSI would attain it.
  • The reverse-engineering construction applies to oscillators whose value depends on only one input and is intended only for the next-price projection.
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Support and resistance5 readingsRelative Strength Index14 readingsCurrent trackPrice-indicator divergence19 readings

A hypothesized next RSI names one close

For a k-period Relative Strength Index, one-day closing prices and the corresponding RSI values are in one-to-one correspondence, so a hypothesized next RSI uniquely determines the next close. If the hypothesized next RSI is above today's RSI, the implied next close is above today's close. If it is below, the implied next close is below today's close.

The reverse-engineering construction applies to oscillators whose value depends on only one input such as high, low, close, open, or volume, and is intended only for the next-price projection.

How the inverse is calculated

The k-period RSI is defined from up-close and down-close series. AUC is the average up-close, the (2k-1)-period exponential moving average of up-closes. ADC is the average down-close, the (2k-1)-period exponential moving average of down-closes. RSI(k)n equals 1 - 1/(1 + AUC(k)n/ADC(k)n).

Given today's close, RSI, AUC, and ADC and a chosen next RSI, X equals (k-1)*ADC0*(RSI1/(100-RSI1)) - AUC0. The next close is C0+X if X is greater than 0, or C0+X*((100-RSI1)/RSI1) if X is less than 0. That next close is the RevEngRSI reading.

A 14-period specification is the conventional lookback used when the inverse is applied on daily, weekly, monthly, or annual closes.

Support, resistance, and divergence as the next RSI

Support and resistance is a previously observed oscillator or price level treated as the hypothesized next RSI reading when converting that reading into a closing-price projection. Divergence is a price-versus-oscillator disagreement used to nominate the next RSI reading that the reverse-engineered formula then converts into a next-close target.

After an important RSI support, resistance, or projected future RSI is identified, a RevEngRSI series for that value tracks price and states the next close at which RSI would attain that value. Combining the inverse with divergences, horizontal support and resistance, and pivots makes the hypothesized reversal level visually explicit as a next-close RSI target.

When price is at an unprecedented high, classical price support-resistance cannot supply a target, whereas an overbought-oversold oscillator can still supply a hypothesized next RSI to invert.

A monthly Hang-Seng illustration

On a monthly Hang-Seng chart, an RSI resistance reading of 86.52 was inverted with a 14-period lookback to project a next-month close of 11635. The index later closed at 11888 with RSI at 86.91, and the inverse of 86.91 implied 11856.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
13 of 16 in the Price-indicator divergence track
20031-1 pp.Next on Price-indicator divergenceScoring open versus resolved relative strength divergencesA standard relative strength index maps a 14-period RS ratio of average up-closes to average down-closes onto a 0-to-100 scale.
All readings on this track · 16 readings
  1. 1989Volume confirmation windows and exponential average construction
  2. 1990Constructing stochastic %K and %D from range position
  3. 1990Build a weekly leading sector composite from scaled transports and financials
  4. 1990Constructing stochastic K and D lines and divergence cues
  5. 1993Relative strength index events depend on the chosen input combination
  6. 1995Constructing a dual-horizon force index
  7. 1996Building a range-normalized divergence index from relative strength index
  8. 1998Treat RSI as a testable filter rather than a trigger
  9. 1999Primary-cycle windows, then stochastic confirmation
  10. 1999Stochastic rules versus buy and hold
  11. 2001Constructing confirmation filters for RSI overbought and oversold extremes
  12. 2003Constructing divergence-equivalent relative strength index and stochastic oscillators
  13. 2003Reverse-engineered RSI as a next-close projection
  14. 2003Scoring open versus resolved relative strength divergences
  15. 2003Bull-and-bear-balance from OHLC bar patterns
  16. 2003Constructing bull and bear balance from session paths
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All 19 readings tagged Price-indicator divergence
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