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1999issue C081-8

Walk-forward evaluation of a polynomial price forecast

A quadratic or cubic polynomial is refit each day on recent average prices to produce a next-day forecast. That curve is only a trend proxy until a percentage-turn rule is checked on a later unused year.

  • A quadratic or cubic least-squares forecast is refit each day on the last T days of average high-low prices and used only to produce a next-day price.
  • The percentage-turn rule becomes a mechanical trading system only after those entries and exits are applied to a later unused year.
  • A three-year in-sample window against a one-year forward test is an experimental ratio, chosen so recent dynamics can appear without distant regimes dominating.
  • If unused segments cannot be modeled usefully, later real-time results are treated as random rather than as a validated mechanical system.
Entries in this reading3 entries
Current trackWalk-forward analysis95 readingsLinear regression112 readingsMechanical trading system158 readings

A daily polynomial forecast

The least-squares forecast is the next-period price from a quadratic or cubic polynomial fitted by minimizing squared vertical error over a lookback of average prices. Each day the polynomial is refit on the last T days of average high-low prices and used to produce a next-day price forecast.

Linear regression, in this workflow, is the least-squares fit that produces the unique polynomial coefficients used as the forecast baseline. Optimization may choose whether the quadratic or the cubic form is the better trend proxy for the series under test.

How the percentage-turn rule enters and exits

The mechanical trading system is a fully specified procedure that maps those fitted coefficients and market state into buy, sell, or stay-out actions without discretionary override.

A percentage-turn rule creates the signals. The system goes long when the forecast curve rises more than a chosen percent from its prior low while short and today's average price exceeds yesterday's forecast. It goes short when the curve falls more than a chosen percent from its prior high while long and today's average price is below yesterday's forecast. Both actions are taken at the next open.

Why the walk-forward window exists

Walk-forward testing is used because the stock's market conditions change. Parameters taken from a prior multi-year window are applied only to a later unused year. That walk-forward window is a rolling in-sample optimization span followed by a later unused segment used only for evaluation.

A three-year in-sample window against a one-year forward test is presented as an experimental ratio, not a unique correct length. The ratio is chosen so the window can capture recent dynamics without being dominated by distant regimes.

What should be recorded from the historical workflow

Prices in the historical workflow are not dividend-adjusted. That omission is treated as a small distortion in parameter choice and walk-forward results and should be recorded.

Charted walk-forward signals show early exits and re-entries around major 1997 and 1998 declines, including a loss after buying the first 1998 bottom before re-entering after the second bottom.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
24 of 50 in the Walk-forward analysis track
20001-3 pp.Next on Walk-forward analysisWalk-forward optimization of regression-slope-angle rulesA linear fit can summarize a chosen price segment as a regression-slope-angle that later long and short rules can read.
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 year199959 readings
All 95 readings tagged Walk-forward analysis
Also on Walk-forward analysis5 readings
1992Constructing forecast models with regression, walk-forward, and robustness1993Constructing walk-forward forecasts with linear and moving-average baselines1993Walk-forward evaluation of monthly yield and real-rate forecasts1996Require both a trend filter and a cycle oscillator before entry1998Evaluating a cubic least-squares currency trend with walk-forward segments