Skip to main content
Track Walk-forward analysis
20 / 50
Search the archiveLibrary
Library

1998issue C051-10

Walk-forward audit of regression trend forecasts

A straight line is fitted to a finite run of daily closes and extended one sampling interval ahead. Five coefficients are then re-estimated on each successive five-year window and applied only to the following year, so later usefulness is judged on the merged one-year holdouts.

  • A least-squares line through a finite run of daily closes is extended one sampling interval ahead to plot a next-close forecast.
  • A long or short is taken only after that forecast curve has already moved by a stated percentage, with entries and exits at the next session open.
  • Lookback length, two percentage trip levels, and two two-session jump levels are re-estimated on each successive five-year window and applied only to the following year.
  • In-sample fitted values alone cannot establish later usefulness; the evaluation sample is the merged sequence of one-year holdouts.
Entries in this reading3 entries
Trend following89 readingsCurrent trackWalk-forward analysis95 readingsLinear regression112 readings

Fitting a next-close forecast

Linear regression, in this workflow, is a least-squares line through ordered prices used as a next-interval forecast. A straight line is fitted through a finite run of daily closes by minimizing the sum of squared vertical distances from each close to the line. The same fit is extended one sampling interval ahead to produce a plotted next-close forecast.

Rules that wait for the curve to move

Trend following here means a long or short only after the forecast curve has already reversed by a stated threshold. A long is taken when that forecast curve has risen by a set percentage from its prior low while short, or when it has jumped by a set percentage versus two sessions earlier. The reverse pair of rules creates the short. Entries and exits are placed at the next session open, so the rules fire only after the forecast curve has already moved.

Scoring the later unseen year

Walk-forward analysis is a rolling in-sample fit followed by a later unseen interval used to score the same rules. Five coefficients are re-estimated on each successive five-year window and then applied only to the following year: lookback length, two percentage trip levels, and two two-session jump levels. In-sample fitted values alone cannot establish later usefulness. The evaluation sample is the merged sequence of one-year holdouts.

Continuous series and chart review

A back-adjusted continuous futures series lets quarterly contracts be treated as one price path, but omitted rollover costs and percentage-scale distortions mean that series is not identical to trading the live expiring contracts. Chart review of the same rules shows delayed signals after turns, weaker stretches in sideways ranges, and a stated need for more walk-forward work on choppy history before live use.

Linear-regression next-day forecast on continuous T-bond futures, 1988–89

A trader following the fitted next-close line would have stayed with the 1988 selloff from the low 70s into the low 61s, chopped through the autumn range, then ridden the mid-1989 melt-up into the mid-74s. The readings come from the red overlay on the source TradeStation daily of the back-adjusted continuous US bond future, not from a printed table.
A trader following the fitted next-close line would have stayed with the 1988 selloff from the low 70s into the low 61s, chopped through the autumn range, then ridden the mid-1989 melt-up into the mid-74s. The readings come from the red overlay on the source TradeStation daily of the back-adjusted continuous US bond future, not from a printed table.US T-bond futures (continuous, CBT) · daily · 1988-02-01T00:00:00.000Z to 1989-06-30T00:00:00.000Z

The overlay begins in February after the T-day fit warms up, not on 1 January 1988. Levels are roll-adjusted continuous-contract prices, not raw front-month prints. Points were sampled about every two weeks from the raster; allow roughly half a point of reading error.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
20 of 50 in the Walk-forward analysis track
19981-13 pp.Next on Walk-forward analysisEvaluating a cubic least-squares currency trend with walk-forward segmentsA 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.
All readings on this track · 50 readings
  1. 1990Three-window walk-forward system evaluation
  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
By fieldTime series and forecasting51 readingsBy year199853 readings
All 95 readings tagged Walk-forward analysis
Also on Walk-forward analysis5 readings
1998Evaluating a cubic least-squares currency trend with walk-forward segmentsTrend following1998Walk-forward evaluation of recursive yen trend signalsTrend following2020Walk-forward and adaptive averages as two tests of the same trendTrend following1992Constructing forecast models with regression, walk-forward, and robustness1993Constructing walk-forward forecasts with linear and moving-average baselines