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1991issue C111

Constructing the true strength index from double-smoothed momentum

The true strength index applies the same two-stage exponential moving average to signed and unsigned one-period price changes, then forms their period-by-period ratio. The construction smooths one-period momentum rather than the price series.

  • The true strength index is constructed by exponentially smoothing one-period price changes, not by smoothing the price series itself.
  • Signed one-period momentum and its absolute value each receive a first-stage 14-period exponential moving average, then a second 3-period pass that completes the double-smoothing.
  • The twice-smoothed signed change is the directional numerator and can be used by itself as a directional indicator.
  • The finished true strength index is the period-by-period ratio of that numerator to the same 14-then-3 sequence applied to the absolute one-day change.
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Current trackExponential smoothing183 readingsMoving average597 readings

Smoothing change, not price

The true strength index is constructed by exponentially smoothing one-period price changes, not by smoothing the price series itself. Those changes are one-period momentum: the signed change from the previous sampling interval to the current one. The matching unsigned magnitude is the absolute value of that change.

The exponential moving average

An exponential moving average is a recursive moving average that blends the newest observation with the prior average. It is a convex blend of the newest observation and the previous average, with a smoothing constant strictly between 0 and 1. That smoothing constant can be taken from a simple moving-average length n as 2 divided by n plus 1.

First-stage averages on both series

Both the signed one-day change and its absolute value receive a first-stage 14-period exponential moving average whose smoothing constant is 2/(14+1), or 0.1333.

The double-smoothing step

Each first-stage series is then passed through a second, 3-period exponential moving average whose smoothing constant is 2/(3+1), or 0.50. That second pass is double-smoothing: a second exponential moving average applied to the output of the first exponential moving average, rather than to the raw series.

Directional numerator and matching denominator

The twice-smoothed signed change is the directional numerator of the index and can also be used by itself as a directional indicator. The denominator is the same 14-then-3 exponential sequence applied to the absolute one-day change.

The finished ratio

The finished true strength index is the period-by-period ratio of those two double-smoothed series: twice-smoothed signed one-period changes over twice-smoothed absolute one-period changes.

True strength index from the 14-day then 3-day double smooth

The oscillator starts pinned at −1.00 while the two double-smoothed series have equal magnitude, then climbs and crosses through zero after the +5.6 up session, finishing near +0.33. Every point is the finished TSI column in the sidebar spreadsheet: each session’s 3-day EMA of the 14-day EMA of one-day change, divided by the same two averages applied to the absolute change.
The oscillator starts pinned at −1.00 while the two double-smoothed series have equal magnitude, then climbs and crosses through zero after the +5.6 up session, finishing near +0.33. Every point is the finished TSI column in the sidebar spreadsheet: each session’s 3-day EMA of the 14-day EMA of one-day change, divided by the same two averages applied to the absolute change.21 January – 1 February 1991 · 1991-01-21T00:00:00.000Z to 1991-02-01T00:00:00.000Z

First-stage alpha is 2/(14+1)=0.1333; second-stage alpha is 2/(3+1)=0.50. Opening EMAs are seeded with that day’s one-period momentum. Two successive printed rows both carry the date 910125, so the series is plotted in table order rather than on a calendar axis. The table stores the raw F/H ratio, not the common 100× scaling.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
14 of 41 in the Exponential smoothing track
19911-19 pp.Next on Exponential smoothingTrue strength index from signed, double-smoothed momentumOne-bar momentum is the current close minus an earlier close, so it carries both the size and the sign of the price change.
All readings on this track · 41 readings
  1. 1984Matching average age across price filters
  2. 1984Residual-impact construction of exponential smoothers
  3. 1988Constructing simple and exponential moving averages as specified filters
  4. 1989Evaluating smoothed free reserves and funds-discount spreads
  5. 1990Integer construction of moving averages and exponential smoothing
  6. 1990Constructing incremental moving average filters
  7. 1991Constructing a double-smoothed stochastic oscillator
  8. 1991Constructing an exponential average from a smoothing weight
  9. 1991Constructing a double-smoothed momentum oscillator family
  10. 1991Competing certainty rules from exponential-average conditions
  11. 1991Hybrid construction of a mechanical timing system from smoothed signals
  12. 1991Constructing an exponential smoother from a moving-average length
  13. 1991Equivalent relative-strength-index constructions from a ratio and from smoothed momentum
  14. 1991Constructing the true strength index from double-smoothed momentum
  15. 1991True strength index from signed, double-smoothed momentum
  16. 1992Constructing exponential averages from simple lookbacks
  17. 1992Constructing exponential averages by the smoothing constant, startup length and lag
  18. 1992Nested range smoothing and windowed high-low damping
  19. 1992A weekly equity stance from the discount-bill spread
  20. 1993Double-smoothed stochastics momentum index construction
  21. 1993Constructing the true strength index with double exponential smoothing
  22. 1994Polarized fractal efficiency with a shared exponential smoother
  23. 1994Five-interval exponential smoothing of ten-interval signed path-efficiency
  24. 1994Hand-ranked price-volume series with stacked smoothing and stochastic
  25. 1995Range expansion filter on multi-horizon averages
  26. 1995The exponential smoothing constant from averaging lag
  27. 1997Construct a nested-average rainbow band and oscillator
  28. 1998Filter stacks that combine a moving average with exponential smoothing
  29. 2002Smoothed relative-strength construction from wilder-averaging and a price prefilter
  30. 2003Reverse-engineered RSI price targets
  31. 2004Piecewise trend quality from moving-average reversals
  32. 2004Nested smoothing recipes versus unaudited oscillator experiments
  33. 2008Weight construction beyond the N-day label
  34. 2010A consensus filter for objective RSI and smoothing construction
  35. 2012Sentiment-zone oscillator from signed closes
  36. 2012Classic RSI one-over-N smoothing versus the standard exponential average
  37. 2013Why exponential smoothing uses two over n plus one
  38. 2015Constructing ratio indicators with moving-average and exponential-smoothing weights
  39. 2015Slow relative-strength index from an exponentially smoothed price
  40. 2017Rebuilding the relative strength index as open-scale buy-sell pressure
  41. 2017Comparing Wilder and exponential smoothing inside a relative-strength index
By fieldIndicators and filters874 readingsBy year1991166 readings
All 183 readings tagged Exponential smoothing
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