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1993issue C011-2

Double-smoothed stochastics momentum index construction

A worked stochastics momentum index measures the close against the midpoint of a lookback range, applies two nested exponential averages to that displacement and to the range width, and forms the finished index from those twice-smoothed series.

  • A worked construction uses a two-period lookback together with two successive 20-period exponential smoothings.
  • The unsmoothed momentum term equals the close minus the midpoint of the lookback high-low range.
  • The lookback high-low width is double-smoothed with the same exponential procedure applied to the momentum term.
  • The finished index equals 100 times the twice-smoothed momentum term divided by half of the twice-smoothed range width.
Entries in this reading3 entries
Current trackExponential smoothing183 readingsStochastic oscillator193 readingsMoving average597 readings

A stochastic-family reading from two series

A stochastic oscillator is a range-normalized reading that locates the close relative to a lookback high-low window and then scales that location to a bounded series.

A stochastics momentum index is a stochastic-family construction that measures the close against the midpoint of the lookback range and divides a double-smoothed version of that displacement by half of the double-smoothed range width.

A worked construction uses a two-period lookback together with two successive 20-period exponential smoothings.

Lookback range and the unsmoothed momentum term

The lookback range is the highest high and lowest low observed over a stated number of sampling periods.

The lookback high is the maximum high over the chosen window, and the lookback low is the minimum low over the same window.

The unsmoothed momentum term equals the close minus the midpoint of that lookback high-low range.

Exponential smoothing, the constant, and seeding

Exponential smoothing is a recursive average that blends each new observation with the prior average using a constant derived from a chosen length.

A moving average is an average of ordered observations over a defined length; here it supplies the length used to set the exponential smoothing constant.

The smoothing constant is the blend weight formed as two divided by one plus the moving-average length. For a length of 20 that constant is 0.095.

Each exponential average is updated as the prior average plus the smoothing constant times the gap between the new observation and that prior average.

The first exponential average is seeded by copying the unsmoothed input because no prior average exists, and recursive smoothing begins on the next observation.

Double smoothing and the finished index

Double smoothing is two nested exponential averages applied in sequence to the same input series.

The lookback high-low width is double-smoothed with the same exponential procedure applied to the momentum term.

The finished index equals 100 times the twice-smoothed momentum term divided by half of the twice-smoothed range width.

The construction is illustrated with a spreadsheet figure that walks through the successive columns of the calculation.

Stochastics momentum index, q=2 and double EMA 20

Finished SMI for the sidebar example, built from the close-versus-midrange term after two nested 20-day exponential averages and scaled by half the twice-smoothed two-day range. Values are taken from the last column of sidebar Figure 1.
Finished SMI for the sidebar example, built from the close-versus-midrange term after two nested 20-day exponential averages and scaled by half the twice-smoothed two-day range. Values are taken from the last column of sidebar Figure 1.Sidebar Figure 1 worked example · daily · 1992-01-06T00:00:00.000Z to 1992-01-29T00:00:00.000Z

Lookback q=2; both smoothings use n=20 so alpha=2/(20+1)=0.095. First row seeds each EMA with the unsmoothed term; smoothing starts on the next bar.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
20 of 41 in the Exponential smoothing track
19931-2 pp.Next on Exponential smoothingConstructing the true strength index with double exponential smoothingThe true strength index is one hundred times the ratio of twice-smoothed one-period momentum to twice-smoothed absolute momentum.
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 year1993106 readings
All 183 readings tagged Exponential smoothing
Also on Exponential smoothing5 readings
1991Constructing a double-smoothed stochastic oscillator1994Hand-ranked price-volume series with stacked smoothing and stochastic1989A variable-sensitivity stochastic built on three-sigma bounds1991Constructing a double-smoothed momentum oscillator family1991Signed midpoint range oscillator from stochastic and Williams