Evaluating weekly price cycles with autocorrelation cutoffs

A two-gate reading of weekly cycle evaluation

Editorial framing presents the archive workflow as a two-gate test. A weekly-close-lag is kept only after an autocorrelation-test finds positive price dependence and the associated chi-square clears a predeclared chi-square-cutoff. The second gate asks whether one dominant-cycle, read with seasonal-analysis on a 13-week grid, can organize the same lengths that independent historical studies already listed.

An autocorrelation-test is a quantitative-model check on ordered price, volume, or breadth observations. It measures dependence at a chosen lag and compares that result with an explicit statistical baseline over a defined sampling interval and lookback. The weekly-close-lag is the spacing, in weeks, between paired closing observations used as a proxy for cyclic length.

The first gate is a chi-square-cutoff

Candidate weekly cycles were retained only when price autocorrelation was positive and the associated chi-square exceeded 3.84, the stated 95 percent cutoff. A 22-week price-to-price lag produced a chi-square of 12.61, well above that 3.84 cutoff. A 23-week lag in the same weekly-close autocorrelation also cleared the 95 percent threshold.

The same research series had found most price and volume auto- and cross-correlations near random, with only a few highly significant chi-square values at scattered lags.

The second gate uses a dominant-cycle and seasonal-analysis

A dominant-cycle step isolates a standout period from ordered market observations so a candidate length can be compared with a baseline and with other reported periods. A 22-week period was treated as a possible fundamental cycle whose harmonics sit near several of the independently listed lengths.

Seasonal-analysis is a portfolio-and-market-context lens that places a single period inside a weeks-to-months regime map. Here it asks whether one short cycle and its harmonics organize a broader grid of listed lengths. Possible cycle lengths were listed as multiples of 13 weeks and aligned against cycle lengths reported in earlier independent studies.

A consensus of the compared studies clustered near 234, 222, 212, 178, 156, 78, 65, 52, 39, 25-26, 12-13, 9-10, 6-7, and 3 weeks. Earlier cycle work had highlighted a 25-26 week period, whereas this weekly-close autocorrelation highlighted 22 and 23 weeks in that same band.

Editorial note: the archive records the cutoff, the two retained lags, and the comparison grid. It does not claim that 22 or 23 weeks replace the 25-26 week highlight. It only shows that both sit in the same band and that a 13-week seasonal grid can be used to organize the listed family of lengths.