Building consensus indicators with correlation and the chi-square test

When overlays leave the ranking open

A chart overlay or an arrow drawn on price leaves the comparison unquantified. Two readers can look at the same indicator and rank it differently, because the review never produces a shared number.

Correlation analysis and the lead-shift

Correlation analysis assigns a signed score between plus one and minus one. The score records how closely an indicator series and a market series move together, including the inverse case. A same-date reading is contemporaneous agreement. It measures agreement, not forecast skill.

Forecast association is built with a lead-shift. The indicator series is advanced a chosen number of sampling intervals and the coefficient is recomputed against later market levels. The shift is then repeated so a useful lead can be searched for.

A five-observation spreadsheet that totals each series, the squares, and the cross-product produced a coefficient of 0.63. That figure was treated as a moderate relationship on the suggested reading scale.

From weekly stance to a batting average

Directional success uses directional coding. Each week is recorded as a constructive, cautious, or undecided stance and is paired with a later up-or-down market outcome. Undecided weeks are ignored. Agreements are then divided by the sum of agreements and disagreements.

That share is the batting average: the share of non-neutral weeks in which a bullish or bearish stance later matches market direction.

The same weekly stance can be scored against market direction one week, five weeks, thirteen weeks, twenty-six weeks, and one year later. Short, intermediate, and long horizons then appear on one record.

A multi-year sample can apply recency-weighting. Rising year weights let a result from ten years earlier count less than a result from a more recent year when hit-rates are totaled.

Testing the tally against chance

A chi-square test on the two-way right-versus-wrong tally asks whether a modest hit-rate could be a chance outcome. Conventional bands are described as once in twenty, once in one hundred, and once in one thousand repetitions.

For two-outcome counts the Yates correction is a half-count adjustment applied to each observed-minus-expected term. The Yates-adjusted chi-square compares each observed frequency with its expected frequency. Listed cutoffs are 3.84, 6.64, and 10.83 for the 95 percent, 99 percent, and 99.9 percent confidence bands.

When a consensus model is allowed

A consensus model is a combined reading assembled only after competing indicators have been scored on the same association and hit-rate yardsticks. Until those scores exist, the blend has no shared numerical scoreboard.