Skip to main content
Track Relative Strength Index
1 / 26
Search the archiveLibrary
Library

1991issue C041

Constructing the relative strength index from seed and recursive averages

The relative strength index is assembled from close-to-close changes, a seed average, and a recursive update. The 0 to 100 reading is a transform of the relative strength ratio, not a comparison with a second market.

  • The relative strength index is a bounded oscillator from zero to 100, formed by transforming the relative strength ratio of average up closes to average down closes.
  • The seed average sums up closes and down closes over the first lookback window and divides each sum by the number of observations, with 14 as the original default.
  • After the seed, an up-close day updates the up-close average by multiplying the prior average by 13, adding today's price change, and dividing by 14, while the down-close average is multiplied by 13/14.
  • The lookback need not stay at 14, and the construction compares a series only with its own recent closes.
Entries in this reading1 entry
Current trackRelative Strength Index261 readings

A bounded transform of two averages

The relative strength index is constructed as a bounded oscillator with a range from zero to 100. The oscillator is a transform of the relative strength ratio, defined as the average of up closes divided by the average of down closes. The transform is 100 minus 100 divided by one plus that ratio.

The construction uses each day's close-to-close change, the signed difference between successive closing prices, to classify an observation as an up close or a down close. The original default lookback is 14 daily observations. The construction compares a series only with its own recent closes, not with a second market or an external benchmark.

How the seed average is formed

The first averages are seeded by summing the up closes over the lookback and dividing by 14, then summing the down closes over the same window and dividing by 14. That first window is the seed average: up closes and down closes are summed separately, and each sum is divided by the number of observations.

The recursive update after the seed

After the seed, an up-close day updates the up-close average by multiplying the prior average by 13, adding today's price change, and dividing by 14. On that same up-close day, the down-close average is updated by multiplying the previous down-close average by 13/14.

That next-period average is the recursive update. It scales the prior average by one less than the lookback, adds the new change when it applies, and divides by the lookback.

Any lookback can form the averages

The lookback length is not required to be 14. Any number of closes may be used to form the averages.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
1 of 26 in the Relative Strength Index track
19911-6 pp.Next on Relative Strength IndexInverting relative-strength-index closes for same-session rulesThe relative-strength-index is constructed as one hundred minus one hundred divided by one plus the relative-strength-ratio of the up-close-average to the down-close-average, with a conventional first window of fourteen periods.
All readings on this track · 26 readings
  1. 1991Constructing the relative strength index from seed and recursive averages
  2. 1991Inverting relative-strength-index closes for same-session rules
  3. 1991Seeded averages and the recursive-update
  4. 1993Restating relative-strength-index parameters after a smoothing change
  5. 1993Relative momentum construction by stretching the relative strength lookback
  6. 1994Constructing relative strength index lookbacks, bands, and confirmation filters
  7. 1994Building the relative-strength-index from signed close changes
  8. 1997Constructing the relative strength index as a bounded up-down close oscillator
  9. 2002Four-line oscillator construction for rule-based entries
  10. 2004Assembling a bounded RSI path
  11. 2004Constructing RSI on highs, lows, and reverse targets
  12. 2004Reverse-engineered RSI as an explicit next-bar price target
  13. 2006Self-adjusting RSI thresholds from the oscillator's own spread
  14. 2006Constructing adaptive overbought and oversold levels for a relative strength index
  15. 2006Relative Strength Index 50-line entry beyond the 70 and 30 extremes
  16. 2007Lock a followable rule set before testing RSI exits
  17. 2008RSI bands as a one-day shift of reverse-engineered levels
  18. 2008Constructing an asymmetrical RSI from adaptive up and down averages
  19. 2010Building a bounded oscillator from a rainbow smoother, relative strength, and inverse Fisher
  20. 2011Two-horizon weekly RSI with moving averages and stops
  21. 2011Percent-offset simple moving average bands with relative-strength confirmation
  22. 2011Fast and slow relative strength index as one mechanical rule book
  23. 2011Price-zone oscillator construction from signed closes
  24. 2015Constructing a zero-lag oscillator against a relative strength index baseline
  25. 2015Relative Strength Index as a baseline in 2015 software listings
  26. 2018Building a Fisherized deviation-scaled oscillator
By fieldIndicators and filters874 readingsBy year1991166 readings
All 261 readings tagged Relative Strength Index
Also on Relative Strength Index5 readings
1985Session windows, volume weights, and divergence in RSI construction1986Constructing bounded relative-strength overlays from oscillator limits1987Constructing the commodity channel, average directional, and relative strength indexes on a shared cycle scale1987Constructing scaled OHLC matrices for study overlays1987Evaluating silver moving averages and RSI by scoring rule