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1994issue C021-13

Constructing MACD from lag-reduced exponential averages

A matching moving average and exponential average share the same long-run lag once the smoothing constant is 2/(w+1). TEMA1 and DEMA2 change how that smoother is built and seeded, then sit inside the usual short-minus-long MACD difference with a nine-period trigger.

  • A conventional moving average of period w has the same long-run lag as a matching exponential average: (w-1)/2, which equals (1-alpha)/alpha when the smoothing constant is 2/(w+1).
  • TEMA1 is three times the first nested exponential average minus three times the second plus the third, a composite required because a locally quadratic path has three regression coefficients.
  • DEMA2 updates a level with alpha and a trend with beta, seeds both from a linear fit on the first w points, and shows large overshoot at trend changes when the trend constant exceeds the level constant.
  • The MACD construction remains a short-minus-long smoother difference with a nine-period exponential average of that difference as the trigger, substituting TEMA1 or DEMA2 for the usual exponential averages.
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Current trackMACD115 readingsExponential smoothing117 readingsMoving average449 readings

Matching the long-run lag

A conventional moving average of period w has the same long-run lag as a matching exponential average. That lag is (w-1)/2, which equals (1-alpha)/alpha when the smoothing constant alpha is 2/(w+1).

TEMA1 as a three-average composite

TEMA1 is defined as three times the first nested exponential average minus three times the second plus the third, and is therefore a composite rather than a plain triple exponential average.

A locally quadratic price path is modeled with three regression coefficients, which is why three nested exponential averages are required before TEMA1 can be formed.

Seeding TEMA1 from an initialization window

TEMA1 seeds are taken from a quadratic least-squares fit on the first 2w observations, then each nested average is started from a closed-form combination of those coefficients and alpha.

That opening stretch is the initialization window: typically one or two averaging periods used to seed recursive averages from a regression rather than from a single first price.

After about two averaging periods the TEMA1 path is essentially independent of the seed, so a first-observation start is adequate when the series is at least twice as long as the longest period w.

On a 26-week window TEMA1 hugs the series more closely than the one-parameter double exponential average, but it overshoots and undershoots more at major long-term turns.

Weekly NASDAQ close, 26-week TEMA1 and DEMA1

On the weekly NASDAQ close the 26-week TEMA1 composite tracks price more tightly than DEMA1, then overshoots and undershoots more at the large trend turns. Series come from the article’s stated seeds and overlay of price with those two 26-week smoothers.
On the weekly NASDAQ close the 26-week TEMA1 composite tracks price more tightly than DEMA1, then overshoots and undershoots more at the large trend turns. Series come from the article’s stated seeds and overlay of price with those two 26-week smoothers.NASDAQ · weekly · 1987-08-14T00:00:00.000Z to 1988-02-05T00:00:00.000Z

TEMA1 seeds from a quadratic fit on the first 2w points (w=26, α=2/(w+1)=0.074): a0=447.753, a1=-7.876, a2=0.146, giving EMA10=569.926, EMA20=714.912, EMA30=882.712 and TEMA10=447.754. DEMA2 seeds on the first w points are S0=448.352 and T0=-6.162.

DEMA2 as a two-constant smoother

DEMA2 splits the smoother into a level updated with alpha and a trend updated with beta. The level mixes the new observation with the previous level plus the previous trend.

DEMA2 initialization uses a linear fit over the first w points to set the starting level and slope rather than using the first raw observation alone.

Keeping the MACD short-minus-long difference

The MACD construction used here remains a short-minus-long smoother difference with a nine-period exponential average of that difference as the trigger, substituting TEMA1 or DEMA2 for the usual exponential averages.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
12 of 80 in the MACD track
19941-1 pp.Next on MACDTEMA1 from nested exponential averages, then a two-horizon MACDTEMA1 is three times a first exponential moving average, minus three times that average applied to its own output, plus the same average applied a third time.
All readings on this track · 80 readings
  1. 1988Rebuild MACD-Mo and MACD-H before treating them as signals
  2. 1989Four-span MACD lookbacks as perishable parameters
  3. 1989Weekly then daily MACD confirmation on individual stocks
  4. 1991Regime-gated MACD and stochastic rules inside a checklist
  5. 1991Constructing MACD signal lines and divergence tests
  6. 1991MACD parameter order and cycle phase lag
  7. 1992Lengthened bond MACD as an equity regime filter
  8. 1992Long-horizon MACD construction from paired exponential averages
  9. 1993Constructing a signed ten-point trend filter
  10. 1994Constructing lag-reduced double exponential averages for MACD
  11. 1994Seeding DEMA2 filters to build a MACD signal
  12. 1994Constructing MACD from lag-reduced exponential averages
  13. 1994TEMA1 from nested exponential averages, then a two-horizon MACD
  14. 1994Constructing entry and exit on a relative-strength MACD
  15. 1994Constructing a relative-strength MACD crossover spreadsheet
  16. 1995Consensus presignal filters for Relative Strength Index, MACD and the Stochastic oscillator
  17. 1997Confirm the MACD turn with price, then exit on the histogram
  18. 1997Reconstructing a stochastic oscillator, MACD, and a triple-smoothed oscillator
  19. 1997Moving-average windows before crossovers and MACD
  20. 1999Second-stage MACD on relative-strength inputs
  21. 1999Constructing MACD from exponential-average spreads for crossover and divergence
  22. 1999Coding candlesticks into numeric indicators
  23. 2001Second-low confirmation with a percentage oscillator and money-flow filter
  24. 2001Constructing MACD from exponential average spreads and a signal line
  25. 2002Separate bounded and trend-following oscillator rules
  26. 2002Sort the regime before assigning MACD and stochastic jobs
  27. 2002Building classic divergence filters from RSI and MACD
  28. 2002Weekly highs and lows as trend gates
  29. 2002Constructing channel-normalized Fisher reversal signals
  30. 2002Affine-price and the Fisher transform as a constructed companion to MACD
  31. 2003Regularized EMA construction with a MACD line and a thrust oscillator
  32. 2003Curvature-penalized exponential averages versus MACD
  33. 2003MACD, moving averages, and a trend filter as one timing system
  34. 2003Fractional MACD and linear-regression reversal construction
  35. 2004Weekly MACD-histogram timing of bear-market rallies
  36. 2004Candlestick triggers filtered by MACD divergence
  37. 2004Staging energy-complex tops with trendline, breakout, and MACD
  38. 2005Selling climax holds versus fails
  39. 2006Treat a sideways Wave as permission before a breakout
  40. 2007MACD with a Stochastic oscillator for spotting trend reversals
  41. 2007Rebuilding an S&P 500 fifth-wave count after a broken target
  42. 2007Constructing MACD, RSI, and stochastic confirmation for futures
  43. 2007MACD histogram divergence needs a confirming close
  44. 2007Write the plan as a stack: ratio, boundary, then oscillators
  45. 2008MACD divergence and Stochastic oscillator confirmation on lumber futures
  46. 2008Assign confirmation, timing, and a stop before a currency pair is tested
  47. 2008Confirm the ten-bagger launch path before the MACD exit
  48. 2008Reading the offloaded evidence file
  49. 2008A Leader companion for MACD direction warnings
  50. 2008Relative strength exits with MACD averages and RSI
  51. 2008Assign one job per indicator in a three-screens rule set
  52. 2008Sequencing RSI, MACD, and average crossovers
  53. 2010Constructing the Schaff Trend Cycle from MACD and a dominant-cycle window
  54. 2010Schaff Trend Cycle as a MACD and Stochastic oscillator combination
  55. 2010Combining Relative Strength Index, the stochastic oscillator, and MACD as slope filters
  56. 2010Short-term wave and ratio clues without direction calls
  57. 2010A precise pullback entry and an unplanned profit-protection exit
  58. 2010Filtering MACD false signals with trendline breaks
  59. 2011Vendor feeds as an input variable in a MACD evaluation
  60. 2012Out-of-the-money versus in-the-money option sensitivity to implied volatility
  61. 2012MACD window tuning as hold-time control
  62. 2012Combining a moving-average crossover with MACD and support-resistance
  63. 2012Testing a published MACD entry with a histogram and signal-line agreement filter
  64. 2012Treat sample systems as a lab before live rules
  65. 2013Constructing moving averages and MACD from one price series
  66. 2013The next-bar price that forces a MACD signal-line cross
  67. 2013Constructing next-bar MACD reversal prices
  68. 2013Constructing inverted MACD reversal prices
  69. 2014Shared-filter combinations of the stochastic oscillator, MACD, and RSI
  70. 2014Square-root lookbacks for combined MACD and RSI
  71. 2015Audit open interest and trend before trusting oscillator crossovers
  72. 2016MACD without a signal line, confirmed by moving-average trend filters
  73. 2016Use RSI, MACD, and a moving average as a market-health consensus
  74. 2016MACD line versus histogram is a display problem first
  75. 2017Weekly and daily MACD on a single daily chart
  76. 2017Weekly and daily MACD as a stacked momentum filter
  77. 2017Nested weekly and daily MACD from paired EMA spreads
  78. 2018Weekly and daily PPO scale versus MACD, with bounded RSI and stochastic readings
  79. 2018Constructing a weekly and daily percentage price oscillator
  80. 2020Constructing Wyckoff tape reading with MACD, moving-average, and RSI filters
By fieldIndicators and filters682 readingsBy year199483 readings
All 115 readings tagged MACD
Also on MACD5 readings
1991MACD parameter order and cycle phase lag1992Long-horizon MACD construction from paired exponential averages1994Constructing lag-reduced double exponential averages for MACD1994TEMA1 from nested exponential averages, then a two-horizon MACD2001Second-low confirmation with a percentage oscillator and money-flow filter