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1998issue C111-13

Evaluating a cubic least-squares currency trend with walk-forward segments

A least-squares cubic forecast is refit each day on recent closes and read one step ahead, then turned into long and short switches. Five successive five-year walk-forward segments selected lookbacks of 40 or 44 days, with most percentage thresholds remaining in a narrow range.

  • A least-squares cubic forecast is refit each day on the last stretch of closes and then read one step ahead as the next-day close estimate.
  • A percent reversal rule goes long when that curve rises by a set percentage from its prior low and goes short when it falls by a set percentage from its prior high, with an optional jump filter on a two-day change in the forecast.
  • Across five successive five-year walk-forward segments, selected lookbacks stayed at 40 or 44 days and most percentage thresholds stayed in a narrow range rather than jumping from window to window.
  • A back-adjusted British pound continuous futures series cannot match live rollover costs or execution slippage, and percentage-of-price rules are distorted by that back-adjustment.
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Trend following89 readingsCurrent trackWalk-forward analysis95 readingsLinear regression112 readings

The least-squares cubic forecast and the switch rules

A rolling least-squares cubic is refit each day on the last T closes and then evaluated one step ahead. That one-step reading is the least-squares cubic forecast for the next close.

The trading procedure follows that forecast. A percent reversal rule goes long when the curve rises by a stated percentage from its prior low and goes short when the curve falls by a stated percentage from its prior high.

An optional jump filter can override those slower switches. It goes long or short when the forecast itself changes by a stated percentage versus the forecast two days earlier.

Walk-forward segments and parameter range

Five successive five-year walk-forward segments, from 1989-1993 through 1993-1997, selected the lookback and the percentage thresholds and then carried those choices onto the next unseen interval.

Those windows selected lookbacks of 40 or 44 days. Most of the percentage thresholds remained in a narrow range rather than jumping from window to window.

In-window summaries from the first two segments

On the first two in-window summaries, the 1989-1993 segment recorded 66 trades with 53 percent profitable and a 2.079 profit factor. The 1990-1994 segment recorded 83 trades with 57 percent profitable and a 2.047 profit factor.

Those same two summaries reported maximum intraday drawdowns of $9,300 and $9,687.50. Average winning trades lasted longer than average losing trades, 23 versus 13 bars and then 18 versus 11 bars.

Editorial reading: those figures describe the windows that chose the parameters. They are not a substitute for asking whether the next unseen interval still used a nearby lookback and nearby percentage thresholds.

A dated buy that remains checkable

A buy dated September 30, 1992, during the decline from about 185 to 130, produced a loss of $8,988. Excluding that episode reduced drawdowns to about $5,000 and worst trades to about $2,000.

Editorial reading: the point of keeping the episode visible is that an out-of-sample turn can still be checked against the price path. Removing it to tidy a drawdown figure is a separate, weaker claim.

British pound continuous futures and cubic forecast, July 1997–May 1998

The last year of walk-forward switches can be checked date by date: the cubic turns with the pound and the 29 May 1998 exit sits near 163. Daily closes and the overlaid one-step cubic were read from the published TradeStation pane for that window, using the printed two-point price scale.
The last year of walk-forward switches can be checked date by date: the cubic turns with the pound and the 29 May 1998 exit sits near 163. Daily closes and the overlaid one-step cubic were read from the published TradeStation pane for that window, using the printed two-point price scale.CME British pound continuous futures · daily · 1997-07-01T00:00:00.000Z to 1998-05-29T00:00:00.000Z

Quotes are Meyers' back-adjusted continuous CME contract, not a single expiry. Raster readings are to the nearest half point. The 1997–98 switches come from the five-year windows that selected a 40-day lookback.

The continuous-contract caveat

The study uses a back-adjusted British pound continuous futures series from January 1, 1989 onward. Such a series cannot match live rollover costs or execution slippage, and percentage-of-price rules are distorted by the back-adjustment.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
21 of 50 in the Walk-forward analysis track
19981-12 pp.Next on Walk-forward analysisWalk-forward evaluation of recursive yen trend signalsA back-adjusted continuous yen series is assembled from quarterly contracts for research, but it cannot match live trading once rollover costs and execution slippage enter the record.
All readings on this track · 50 readings
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  2. 1990Building the construction layer of a mechanical trading system
  3. 1991Constructing walk-forward neural trading rules
  4. 1991Constructing neural trading systems from facts to walk-forward
  5. 1992Walk-forward evaluation of stop overlays on average crossovers
  6. 1992Audit mechanical system tests for fills and regimes
  7. 1993Walk-forward evaluation of monthly yield and real-rate forecasts
  8. 1993Constructing walk-forward forecasts with linear and moving-average baselines
  9. 1993Walk-forward hybrid rules for intermarket forecast stacks
  10. 1994Neural-net construction as a mechanical trading-system problem
  11. 1995Constructing an intermarket neural net trading system
  12. 1996Weekly market breadth as one procedure on an unused window
  13. 1996Walk-forward evaluation of gold-index bond-fund rules
  14. 1996Evaluating weekday-in-month filters for index day trades
  15. 1996Require both a trend filter and a cycle oscillator before entry
  16. 1997Walk-forward windows as a diagnostic of parameter instability
  17. 1997Walk-forward validation of a market-breadth timing rule
  18. 1997Sunspot spikes and walk-forward evaluation of an adaptive cycle rule
  19. 1997A walk-forward check for bond-breadth timing
  20. 1998Walk-forward audit of regression trend forecasts
  21. 1998Evaluating a cubic least-squares currency trend with walk-forward segments
  22. 1998Walk-forward evaluation of recursive yen trend signals
  23. 1999Personal system design under crowd psychology
  24. 1999Walk-forward evaluation of a polynomial price forecast
  25. 2000Walk-forward optimization of regression-slope-angle rules
  26. 2001Construct a winter seasonal window as one procedure
  27. 2001Inspectable rules when system write-ups dry up
  28. 2002Evaluating mechanical systems before position sizing
  29. 2003Walk-forward construction of rule-based market-position systems
  30. 2007Evaluating metal seasonal windows across regimes
  31. 2007Evaluating mechanical timing systems against hold baselines
  32. 2011Walk-forward reoptimization as a system design gate
  33. 2011Evaluate generated systems on holdouts, then add stops
  34. 2012Walk-forward analysis and out-of-sample tests for a mechanical trading system
  35. 2012Personality-first trading system design
  36. 2012Scorecard-first mechanical system construction
  37. 2012Constructing an advancer-decliner moving average for market breadth
  38. 2012Formula search as mechanical system construction
  39. 2013Identity-first system construction
  40. 2013Construct a swing system from bias rules to walk-forward
  41. 2014Evaluate mechanical stock systems with stops and walk-forward
  42. 2014Walk-forward velocity filters on noisy intraday trends
  43. 2015Event-predictability versus position-constrained rules
  44. 2015Constructing mechanical systems for walk-forward tests
  45. 2016When a tested system must be retired
  46. 2016Walk-forward metric filters and chance-level checks for selected inputs
  47. 2018Evaluate mechanical trading systems without catalog rankings
  48. 2019Phased stop construction from entry risk to trailing exit
  49. 2020Stockpiling simple ideas for mechanical system construction
  50. 2020A pretty first draft is not a walk-forward waiver
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