Skip to main content
Track Moving-average crossover
37 / 57
Search the archiveLibrary
Library

2007issue C021-10

Anticipating moving-average crossovers one bar ahead

A K-period simple moving average is a convex combination of the newest close and the previous (K-1)-period average, so tomorrow's averages are linear in the still-unknown close. Setting those one-step-ahead averages equal produces a unique threshold close that can be compared with the live close on the current bar.

  • A K-period simple moving average is a convex combination of the newest close and the previous (K-1)-period average, so tomorrow's averages are linear in the still-unknown close.
  • Setting the two one-step-ahead averages equal yields a unique threshold close; for 20- and 30-period averages it is 58 times the 29-period average minus 57 times the 19-period average.
  • Comparing the live close with that threshold is intended to flag, on the current bar, whether the two simple moving averages will meet on the next bar.
  • The construction leaves the simple moving average unweighted. The one-bar reduction in lag comes from the algebraic forecast of the meeting price, not from an exponential or weighted average.
Entries in this reading3 entries
Current trackMoving-average crossover108 readingsLinear regression112 readingsMoving average449 readings

Two averages and one unknown close

A moving-average crossover is a signal that fires when a shorter-period simple moving average meets a longer-period simple moving average. It is conventionally read after the close that produces the touch.

A simple moving average is the unweighted mean of the last K closes. Equivalently, it is a convex combination of the newest close and the previous (K-1)-period average. The construction here leaves that definition unchanged and solves for the threshold close: the unique next-session close that would make two chosen simple moving averages equal.

A convex combination of the newest close

A K-period simple moving average can be written as a convex combination of the newest close and the previous (K-1)-period simple moving average, so tomorrow's averages are linear in the still-unknown close.

The unique threshold close

Setting the two one-step-ahead simple moving averages equal and solving for the unknown close yields a unique threshold close of the form (P*(K-1)*MA(K-1) - K*(P-1)*MA(P-1))/(K-P). That value is obtained by rearranging the recursive simple-moving-average update.

For the concrete pair of 20- and 30-period simple moving averages the threshold close simplifies to 58 times the 29-period average minus 57 times the 19-period average.

A flag on the current bar

Comparing the live close with that threshold close is intended to flag, on the current bar, whether the two simple moving averages will meet on the next bar.

The average stays unweighted

The construction leaves the simple moving average unweighted. The one-bar reduction in crossover lag comes from the algebraic forecast of the meeting price, not from switching to an exponential or weighted average.

The same formula on a platform

Platform implementations treat the same threshold-close formula as a plotted level, a predicted-versus-actual cross marker, and a tabulated event log rather than as a rewritten moving-average definition.

A check against the next close

Linear regression, in this setting, is an ordinary least-squares fit of the threshold-close series against subsequent price. It is used as a quantitative check that the solved level tracks the next close rather than as a trading rule.

Average profit per S&P 100 name: one-bar-early TC entry versus waiting for the SMA cross

On every fast/slow pair in the Wealth-Lab optimizer table, buying when the solved tomorrow-close crossed price (strategy 0) made more average profit per S&P 100 name than waiting for the moving averages themselves to cross (strategy 1). The 15/40 pair led at 454.55 dollars versus 94.04 if you waited; 15/30 even lost money if you waited. Figures are the [Avg] rows from that table, five years of daily bars, 10000 dollars per trade, commissions ignored.
On every fast/slow pair in the Wealth-Lab optimizer table, buying when the solved tomorrow-close crossed price (strategy 0) made more average profit per S&P 100 name than waiting for the moving averages themselves to cross (strategy 1). The 15/40 pair led at 454.55 dollars versus 94.04 if you waited; 15/30 even lost money if you waited. Figures are the [Avg] rows from that table, five years of daily bars, 10000 dollars per trade, commissions ignored.S&P 100 · Daily · 2002-01-01T00:00:00.000Z to 2007-12-31T00:00:00.000Z

Strategy 0 buys when tomorrow's close crosses under the live close, holds overnight, and sells the next close. Strategy 1 buys after the SMA cross and sells that same close. Fast lengths 10, 15, 20; slow lengths 30, 40, 50. Fixed 10000-dollar sizing.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
37 of 57 in the Moving-average crossover track
20071-10 pp.Next on Moving-average crossoverLead-series moving-average crossovers with a stochastic and relative strength indexTwo unequal simple moving averages invert into a lead series: a close that meets the lead series is a predicted cross, and the later change of order is the confirmed cross.
All readings on this track · 57 readings
  1. 1988Constructing moving averages: weights, smoothing and crossovers
  2. 1988Constructing breadth and average trend states
  3. 1989Evaluating an always-in-the-market moving-average crossover
  4. 1989Constructing symmetric market-breadth ratio accumulators
  5. 1989Objective crossover tests of Fibonacci wave ratios
  6. 1990Volume-adjusted moving average construction
  7. 1991Constructing a mechanical crossover on a synthetic price series
  8. 1991A two-speed breadth reading for intermediate market direction
  9. 1992A Deutschemark yield map with dual-average and relative-strength timing
  10. 1992Confirming currency-fund trends with a crossover and a filter
  11. 1992A moving-average slope filter for crossover signals
  12. 1992Occupancy and split-sample tests for average crossovers
  13. 1994Gold-mining seasonality and bond-fund duration switching
  14. 1994Price oscillator from two moving averages
  15. 1995Explicit exponential weights and binary entry filters
  16. 1996Currency futures crossover with slope, bond filter, and stop
  17. 1996Two-market average crossover entry with a fixed stop
  18. 1997Construction of a filtered three-average crossover
  19. 1998Two-group exponential average compression as a trend filter
  20. 1998Constructing r-squared trend filters with dual lookbacks
  21. 1998Moving-average length is a habit, not a secret
  22. 1999Solving the close that triggers a moving-average crossover
  23. 2000Kagi yang and yin control versus crossover noise
  24. 2000Constructing simple moving average crossover filters
  25. 2000Building a vertical-horizontal filter to gate trend signals
  26. 2000Two-average crossover as a check on trend following
  27. 2003Stacked exponential-average retracement entries and extreme stops
  28. 2003Evaluating oscillator thresholds against optimized crossovers
  29. 2004Constructing a semicycle trend-quality filter
  30. 2004Commodity subgroups labeled by crossover, support, or convergence
  31. 2004Full-window evaluation of crossover trend systems
  32. 2004Two-average trend filters as a classroom critique of indicator stacking
  33. 2005Three-layer confirmation from a moving-average cross, candles, and Q-stick
  34. 2005Charting put prices beside an equity breakdown
  35. 2005Range-gated moving-average crossover construction
  36. 2007Anticipating a simple-average crossover with a threshold-close
  37. 2007Anticipating moving-average crossovers one bar ahead
  38. 2007Lead-series moving-average crossovers with a stochastic and relative strength index
  39. 2007Next-bar SMA crossover hypotheses from theoretical crossing values
  40. 2007Anticipating a moving-average crossover before confirmation
  41. 2007A three-horizon moving-average stack as a construction problem
  42. 2007Confirming trend with regression slope and r-squared
  43. 2008Constructing a multi-timeframe smoothed crossover
  44. 2008Best-day clusters versus trend filters
  45. 2008Allied markets as a confirmation gate for crossover and breakout signals
  46. 2008Weekly exponential-average crossover as a mechanical trend case study
  47. 2010Evaluating a 200-day crossover as long, short, and stand-aside rules
  48. 2010Read a 10-and-40 trend on two neighboring time frames
  49. 2012Sampling unit as a first-class parameter on dual simple moving averages
  50. 2012Constructing index-ETF entries from volatility-index persistence
  51. 2013Moving-average baselines versus crossover signals
  52. 2013Constructing a typical-price and heikin-ashi crossover as one mechanical procedure
  53. 2016A three-gate checklist for longs after a sharp drop
  54. 2016Weekly inflation-ratio crossover for commodity regimes
  55. 2017Normalized Laguerre zero-axis warning as a two-marker construction
  56. 2019Range-weighted construction of an adaptive exponential moving average
  57. 2020Construct a second-pullback entry after a moving-average crossover
By fieldIndicators and filters682 readingsBy year200773 readings
All 108 readings tagged Moving-average crossover
Also on Moving-average crossover5 readings
1988Constructing breadth and average trend states1998Constructing r-squared trend filters with dual lookbacks2004Evaluating P/E overlays with matched crossovers2007Confirming trend with regression slope and r-squared1988Constructing moving averages: weights, smoothing and crossovers