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1991issue C091-8

Quadratic trend, residual oscillator, and a secondary cycle calendar

After the mid-January 1991 break, June gold was framed between support near 355 and resistance at 376. A second-degree least-squares baseline was fitted to daily closes so the leftover series could be read as a banded residual oscillator, while 12-day and 24-day low spacings only sketched later dates. The written entry procedure still fired when that calendar disagreed.

  • After the mid-January 1991 break, the working near-term range for June gold sat between long-term support near 355 and newly formed resistance at 376.
  • A second-degree least-squares baseline fitted to daily closes after January 15 left residuals between 7.01 and -8.28, with limit bands at plus or minus 3.82.
  • The written entry procedure reversed on the first turn beyond a limit band, applied a trend-direction filter, and also acted on residual-versus-price divergences.
  • Dominant-low spacing of about 12 or 24 days only sketched later lows. A signaled rule still fired when that calendar disagreed, and model refresh followed those trades or a baseline cross.
Entries in this reading3 entries
Current trackLinear regression112 readingsDominant cycle detection119 readingsRule-based entry174 readings

A working range after the break

After the mid-January 1991 break, the working near-term range for June gold was framed between long-term support near 355 and newly formed resistance at 376.

Short-term lows in the plotted gold series recurred about 12 or 24 days apart, and those spacings were later used to sketch future low dates.

Three layers, kept separate

Editorial reading: teach the work as three layers that do not collapse into one signal. First fit a least-squares baseline, a polynomial chosen so the sum of squared gaps from observed prices is minimized, with the degree set by how many turning points the series is allowed to contain. Next read the leftover series as a residual oscillator, an overbought or oversold excursion around that baseline. Last, keep a dominant-low spacing calendar that only sketches later turning dates and does not authorize a trade.

The archive then attaches one written entry procedure to the residual oscillator and its limit bands. Editorial reading: that procedure is the trigger. The calendar may disagree and the rule still fires.

The least-squares baseline

A second-degree least-squares fit P = 390.52 - 0.77202 * t + 0.0055339 * t^2 was applied to daily closes after January 15 so the baseline could contain one turning point.

The fitted equation was not to be projected far beyond the sample. A new least-squares fit was required whenever prices crossed the current baseline and immediately after trades from the reversal or divergence rules.

Residual oscillator and limit bands

Residuals of that fit stayed between 7.01 and -8.28, and those extremes often lined up with local turning points in the original closes.

Limit bands were placed at plus or minus 3.82 around the fitted curve, one-quarter of the residual range, with 81 percent of points below the upper band and 83 percent above the lower band. A first reversal beyond a band is the entry trigger.

The written entry procedure

The written entry procedure shorted on the first downturn after a move above the upper band, bought on the first upturn after a move below the lower band, traded only with the trend unless the trend was flat, and also acted on residual-versus-price divergences.

The trend-direction filter accepts a residual signal only when it agrees with the current baseline slope, or in both directions when that slope is flat.

Cycle dates stay secondary

Dominant-low spacing, the recurring interval between successive short-term lows, was used only to sketch later turning dates. The cycle date estimate was treated as secondary: a signaled rule was to be executed even if the low-to-low calendar disagreed.

Model refresh means recalculating the fit after a signaled trade or after raw prices cross the current baseline, because added observations change the coefficients.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
9 of 43 in the Linear regression track
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All readings on this track · 43 readings
  1. 1990Constructing dollar baselines from rates, inflation, and residuals
  2. 1990Constructing a nominal index value from forward earnings and fitted yield
  3. 1990Constructing a nominal index price from earnings and a fitted yield
  4. 1990Endpoint-pinned price paths are not forecasts
  5. 1990Constructing least-squares polynomial smoothers
  6. 1991Endpoint growth rates versus linear-regression consistency
  7. 1991Out-of-sample checks for linear growth fits
  8. 1991Trend as persistence, not a straight line
  9. 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
  10. 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
  11. 1991A least-squares trendline from ordered prices
  12. 1992Constructing log-linear growth and reliability screens
  13. 1992Constructing log-linear growth-rate baselines
  14. 1992Next-session high, low, and close from rolling linear regression
  15. 1993Auditing an index price-earnings multiple with short-rate regression
  16. 1994Regression-seeded nested exponential price filter
  17. 1994Constructing the double exponential average from lag cancellation
  18. 1994Evaluating money supply as a linear leading-index baseline
  19. 1995Constructing least-squares trend channels
  20. 1995Linear baseline holdout checks for annual bill-rate forecasts
  21. 1995Projection bands from high and low regression slopes
  22. 1995Evaluating a least-squares end-point moving average on a known test series
  23. 1996Constructing an endpoint moving average from a least-squares line
  24. 1996Scoring equity path consistency with a k-ratio overlay
  25. 1996Evaluating month-end yield gaps for equity regimes
  26. 1996Constructing session-indexed standard error bands
  27. 1998Evaluating linear regression baselines for index valuation
  28. 1998R-squared as a two-state trend filter from a price-time fit
  29. 2000Second-order moving-average lag correction
  30. 2002Price regression line versus beta for index tracking
  31. 2003Regression slope with an r-squared trend confidence gate
  32. 2003Constructing finite-volume-element divergence with slope comparison
  33. 2004Building a daily score from regression, retracement, and volume
  34. 2004Constructing least-squares trendlines from ordered prices
  35. 2007Rectangle breakout targets beyond height
  36. 2007Confirming a price trend with regression slope and r-squared
  37. 2008A linear-regression angle assembled as one trend filter
  38. 2010A two-state swing machine from four running extremes
  39. 2016Score oil-complex tightness before divergence or regression
  40. 2017Nikkei-yen intermarket divergence as a regime case study
  41. 2017Constructing Calmar ratio and linear regression baselines
  42. 2019Pair-trade layer construction versus average-spread management
  43. 2020A convolution slope built from nested linear regression
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