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1992issue C051-15

Constructing a double-smoothed true strength index

Build the true-strength-index as a construction sequence: form one-period-momentum, apply double-exponential-smoothing to the signed series and to its absolute value, then read a slow pair and a fast pair as separate length choices rather than as a finished system.

  • One-period-momentum is the signed change from the prior close to the current close, so an up-move is positive and a down-move is negative.
  • The true-strength-index divides double-smoothed one-period-momentum by double-smoothed absolute momentum and scales the ratio by one hundred so the reading stays comparable when the price level changes.
  • The divergence-indicator is the unnormalized numerator; stretching or shortening the first smoothing changes whether that curve tracks price or shows divergences.
  • A fast-slow-pairing states regime with a longer double-smoothing pair and timing with a shorter pair, so each window can be inspected before a crossover is treated as a rule.
Entries in this reading3 entries
Current trackMomentum strategy103 readingsExponential smoothing117 readingsMoving average449 readings

Start from one-period momentum

One-period-momentum is the current close minus the prior close. An up-move is a positive value and a down-move is a negative value.

That signed change is the series later averaged in both the numerator and the denominator.

Write the two-pass smoother

The true-strength-index is built by applying two successive exponential averages to one-period-momentum in the numerator. The same double-exponential-smoothing is applied to the absolute value of that momentum in the denominator. The ratio is then multiplied by 100.

Double-exponential-smoothing means a second exponential average applied to the output of a first exponential average of the same series. The smoothing-constant is the exponential weight estimated as two divided by one plus the chosen lookback length.

Isolate the absolute-value normalizer

The absolute-value denominator is included so the output stays in a bounded range, illustrated as plus and minus 100. That shared numeric scale remains comparable when the price level changes.

The unnormalized numerator of the same construction is the divergence-indicator: successive exponential averages of one-period-momentum without the absolute-value scale.

Read the first and second lengths

One illustrated specification uses first and second smoothings of 25 and 13 periods. A 7-period exponential average of the index is then used as a signal-line, marking candidate turning points by crossover with the bounded series.

A 300-period first smoothing of momentum with the second length set to 1 produces a curve that follows the shape of price. The bounded index compresses amplitude and can show divergences the unnormalized series does not.

Adding a 9-period second exponential pass to that 300-period momentum series removes short fluctuations while keeping turning points close to those of a comparable exponential average of the close.

Reducing the first window from 300 to 100 periods with a 9-period second pass introduces divergences that were absent at the longer window. The unnormalized and bounded series then share the same shape except for scale.

True strength index from the 14-then-3 calculation worksheet

Ten daily sessions from 21 January 1991 through 1 February 1991 show the constructed index as the ratio of twice-smoothed signed one-day momentum to twice-smoothed absolute momentum. The reading sits at −1.00 while the first changes are negative, then rises and crosses zero on 30 January once the second exponential pass of signed momentum turns positive. Figures are copied from the Calculating TrSI sidebar table, not traced off a plotted curve.
Ten daily sessions from 21 January 1991 through 1 February 1991 show the constructed index as the ratio of twice-smoothed signed one-day momentum to twice-smoothed absolute momentum. The reading sits at −1.00 while the first changes are negative, then rises and crosses zero on 30 January once the second exponential pass of signed momentum turns positive. Figures are copied from the Calculating TrSI sidebar table, not traced off a plotted curve.Daily · 1991-01-21T00:00:00.000Z to 1991-02-01T00:00:00.000Z

The first pass is a 14-day EMA (α = 0.1333) and the second pass is a 3-day EMA (α = 0.50). The sidebar reports TSI as column F divided by column H and does not apply the ×100 factor written in the article formula. The 4 February 1991 row lists only formulas and is omitted.

Split a slow regime layer from a fast timing layer

One illustrated two-layer procedure uses a fast-slow-pairing. Trend is defined with double smoothing of 100 and 20 periods. Entries and exits are selected with a faster pair of 20 and 6 periods.

An alternative construction keeps the 20-and-6 index for timing and defines trend as a 20-period exponential average of that same fast series.

Suggested construction pairs for experimentation are 20 and 6, 40 and 20, and 80 and 40. They are presented as lag-versus-smoothness trade-offs rather than universal settings.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
10 of 51 in the Momentum strategy track
19931-9 pp.Next on Momentum strategyWhen momentum structure and breadth break togetherMomentum is the relative change in price or breadth over a chosen interval, read against a moving-standard as an internal map of market action rather than only as a check on moving averages.
All readings on this track · 51 readings
  1. 1984Half-cycle differencing for momentum signals
  2. 1987Relative strength evaluation under competing optimization criteria
  3. 1988Weekly MACD as a two-clock momentum confirmation stack
  4. 1989Equal-weight zero-cross from smoothed spreads
  5. 1989Testing relative-strength-index reversal rules against trend continuation
  6. 1989Smoothed three-day futures filter for index option bounces
  7. 1989Cycle-length windows for momentum, Relative Strength Index, and stochastic construction
  8. 1991Filtered rally magnitude as a bull-regime breakout
  9. 1992Constructing true strength from double-smoothed momentum
  10. 1992Constructing a double-smoothed true strength index
  11. 1993When momentum structure and breadth break together
  12. 1993Constructing double-smoothed range and momentum oscillators
  13. 1993Constructing a two-parameter relative momentum index
  14. 1993Building a bounded momentum oscillator with RSI smoothing
  15. 1993Two-speed oscillators with divergence and trendline gates
  16. 1993Constructing a relative momentum index from the relative strength index
  17. 1994Constructing daily advance-decline breadth tools
  18. 1994Building a composite regime score from monetary climate and weekly trend
  19. 1994Averaging Relative Strength Index and the stochastic oscillator into one reversal oscillator
  20. 1995Dividend-yield regression as a hold versus momentum gate
  21. 1996Jump and hold filters for long-term Treasury yield direction
  22. 1997Constructing extendedness from a 10 percent swing filter
  23. 1997A range-expansion oscillator that can refuse its own stretch
  24. 1997RSI trend permission and Fibonacci pullback rules
  25. 1998Nested midpoint construction for a range-normalized oscillator
  26. 1999Evaluating Relative Strength Index momentum with zero-line and threshold rules
  27. 1999Treat RSI and momentum as three mechanical procedures
  28. 2000Thrust strength figure from moving-average swings
  29. 2001Constructing a non-range-bound balance of market power score
  30. 2004Cleaned breadth oscillator and new-high divergence: a swing-market case file
  31. 2004Evaluating advance-issues-momentum on a fixed-symbol-basket
  32. 2004Constructing a trend filter from two adjacent high-low windows
  33. 2006A dollar-versus-commodity extreme as a regime case
  34. 2008Zero-centered stochastic bands and bracket stops
  35. 2012Evaluating engulfing momentum across hold windows
  36. 2012Staged stops as one mechanical entry and exit procedure
  37. 2012Stacking a relative-strength-index forecast, a trend filter, and long-only momentum
  38. 2013Constructing fair-value filters from averages and momentum
  39. 2014Constructing a multi-window slope divergence entry
  40. 2015Bandedge trend filter construction with inverse crossover rules
  41. 2017Opposite rules for index price and volatility momentum
  42. 2018A three-state overlay that colors a trend only after the line clears the bar
  43. 2018Half-cycle relative-strength index with a Fisher map for cyclic reversals
  44. 2018Emotion as a rule input when momentum breaks
  45. 2018Two-bar body expansion as a momentum breakout construction
  46. 2019Pair a two-day high breakout with a volume-weighted exit on the same chart
  47. 2020Building reflex and trendflex cross and extreme entry rules
  48. 2020Construct a dual-series price momentum oscillator overlay
  49. 2020A multi-timeframe stochastic as a panel of weekly voters
  50. 2020Centerline crossovers that compare index momentums
  51. 2020Multi-timeframe stochastic voting as one mechanical rule
By fieldIndicators and filters682 readingsBy year1992115 readings
All 103 readings tagged Momentum strategy
Also on Momentum strategy5 readings
1989Equal-weight zero-cross from smoothed spreads1989Smoothed three-day futures filter for index option bounces1992Constructing true strength from double-smoothed momentum1993Constructing double-smoothed range and momentum oscillators1985Constructing excess and momentum difference-curve oscillators