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1988issue C041-2

Constructing a lead-aware correlation coefficient

The correlation coefficient is assembled from five column totals and the observation count. Shifting one series by a chosen number of intervals and recomputing the score tests whether the relationship is contemporaneous or leading.

  • The correlation coefficient is a signed score bounded by +1 and -1 that states how closely two paired series move together.
  • Five column totals, plus the observation count, assemble the coefficient as a ratio whose numerator is the observation count times the cross-product total minus the product of the two series totals.
  • A lead-lag shift offsets one series before recalculation to test whether agreement appears in advance rather than at the same time.
  • On the interpretation scale used with the worked example, a coefficient of 0.63 is treated as a moderate association.
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Current trackCorrelation analysis52 readings

What the coefficient measures

The correlation coefficient is a signed measure of association between two series and ranges from +1 to -1. It is a signed score that states how closely two paired series move together.

A reading near +1 means the paired series typically move in the same direction. A reading near -1 means they typically move in opposite directions. A reading near zero means no clear relationship is evident.

How the score is assembled

Construction uses five columns: the two raw series, the square of each series, and the pairwise product. Those columns are totaled and the observation count is recorded. The five spreadsheet aggregates, together with the observation count, are the column totals used to assemble the coefficient.

The coefficient is formed from those column totals and the observation count as a ratio. The numerator is the observation count times the cross-product total minus the product of the two series totals.

A worked numerical example evaluates to 0.63. On the accompanying interpretation scale that reading is labeled moderate correlation and is treated as a moderate association.

How a lead is tested

To test whether one series leads another, the first series can be shifted by a chosen number of intervals and the coefficient recomputed against later values of the second series.

That lead-lag shift is an offset applied to one series before recalculation. It is used to test whether agreement appears in advance rather than at the same time.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
1 of 37 in the Correlation analysis track
19891-6 pp.Next on Correlation analysisA precious-metal price as a changing intermarket equationStepwise multiple linear regression estimated a metal’s mean price from related series such as inflation gauges and, when they still helped, foreign-exchange rates.
All readings on this track · 37 readings
  1. 1988Constructing a lead-aware correlation coefficient
  2. 1989A precious-metal price as a changing intermarket equation
  3. 1990Two clocks for copper: a factor regime, a regression baseline, and leftover moving-average timing
  4. 1990Earnings yield, rate correlation and regression for equity value
  5. 1991Name the window, then combine leaders
  6. 1991Constructing a two-market linear correlation check
  7. 1991Constructing a commodity-bond correlation regime filter
  8. 1992Building intermarket context with linear correlation
  9. 1993Inverse-scale overlays as a gold-equity regime filter
  10. 1994Constructing seasonal slots from windows, analog years, and implied volatility
  11. 1995Pin one reference close and roll companion correlations as an overlay
  12. 1995Rolling correlation windows for shifting intermarket regimes
  13. 1998Gold as a cross-market regime barometer
  14. 1999The gold-bond inverse is a regime, not a cause
  15. 1999A nested lag test of gold leading bond yields
  16. 1999Constructing spreads from stock and intermarket correlation
  17. 2000Evaluating headline versus food-and-energy-excluded CPI as bond-yield context
  18. 2005A late EUR/USD fifth wave tested by the Bund-Treasury gap
  19. 2006Intermarket dislocation as context for short-horizon momentum
  20. 2008Map ordinary 12-month outcomes before stacking valuation, rates, and seasonality
  21. 2008A clean-energy theme inside the oil-and-energy regime
  22. 2014Quantitative-easing overlays as fragile belief regimes
  23. 2015Three intermarket checks from the late-2014 crude decline
  24. 2015Basket construction via rank, correlation, and locked rules
  25. 2015Construct a CAD-oil pair from percent-of-range Bollinger maps
  26. 2015CAD/USD and crude: first the correlation, then the band gap
  27. 2017Correlation regime versus moving-average crossover for S&P 500 exposure
  28. 2017Updating intermarket systems after correlation shifts
  29. 2017Constructing a correlation-divergence regime filter for yen and Nikkei context
  30. 2018Clustered negative troughs in an energy-index pairwise correlation
  31. 2018Filter pairwise-correlation before reading an intermarket regime
  32. 2018Moving-average supports in the March 2018 correlation shock
  33. 2020Bond spreads as an equity regime lens
  34. 2020Crash-protection folklore as a correlation regime question
  35. 2020Constructing a bounded correlation-trend-filter
  36. 2020Constructing a correlation-to-line trend filter
  37. 2020Bitcoin correlation regimes across equities and gold
By fieldStatistical tests59 readingsBy year198866 readings
All 52 readings tagged Correlation analysis
Also on Correlation analysis5 readings
1988Building consensus indicators with correlation and the chi-square test1989A precious-metal price as a changing intermarket equation1990Two clocks for copper: a factor regime, a regression baseline, and leftover moving-average timing1990Earnings yield, rate correlation and regression for equity value1991Constructing a commodity-bond correlation regime filter