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1988issue C091

Event-triggered chi-square tests for jittered serial links

A diagnostic order of operations for coded money-supply and S&P 500 extremes: start an event trigger, collect a waiting monthly histogram, score it with a chi-square test against an independence baseline, and only then ask why an autocorrelation test can miss the same serial link when timing jitter is present.

  • Code money-supply and S&P 500 extremes, then use an event trigger so sequential collection can build monthly histograms of later matching extremes.
  • An independence baseline expects an even monthly spread; the collected histograms for the first, second, and fifth sequential large S&P 500 declines after a large money-supply increase were not even.
  • A chi-square test of the fifth sequential decline histogram against the fifth sequential advance histogram, adjusted for how often each code appeared, found the histograms dissimilar and was treated as evidence of a serial interrelationship.
  • An autocorrelation test on the same ordered series can miss that link when timing jitter makes the lag irregular, including in the three-event sequence that waits through an intervening decline before a later advance.
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Current trackAutocorrelation test23 readingsChi-square test44 readings

The evaluation asked whether coded money-supply extremes and coded S&P 500 extremes behave as independent series.

As an editorial guide, do not begin with an autocorrelation test on the raw ordered observations. Code the extremes first, let an event trigger start a waiting histogram, and score that histogram before asking why a serial screen can miss the link.

Code extremes and trigger a waiting histogram

A large money-supply increase served as an event trigger, a coded extreme that starts the wait for a later coded extreme in the same or another series. Sequential collection then recorded the month of the first, second, or later matching extreme after that trigger.

Under an independence baseline, months of the first large S&P 500 decline after a large money-supply increase would be evenly spread if the two series had no serial link. The collected histogram was not even.

Uneven monthly counts also appeared for the second and the fifth sequential large S&P 500 declines after that same money-supply trigger.

A compound trigger, a large money-supply increase and then a large S&P 500 decline, was used to collect the next large S&P 500 advance.

Score the histogram with a chi-square test

A chi-square test is a comparison of event-count histograms, after a defined sampling interval and lookback, used to judge whether two coded series match an independence or matched-code baseline.

The archive compared the fifth sequential large S&P 500 decline histogram with the fifth sequential large S&P 500 advance histogram, adjusted for how often each code appeared, and found the histograms dissimilar.

That chi-square dissimilarity was treated as evidence of a serial interrelationship between the two series rather than independence.

As an editorial guide, run that histogram contrast, including a score against the even-month independence baseline, before turning to any other screen on the same ordered series.

An autocorrelation test is a classical serial or cross-correlation check on ordered observations. The archive argued that serial and cross-correlation tests would be unlikely to detect these links because of timing jitter, the irregular delay between a trigger and the matching later extreme.

The same timing-jitter limitation was said to apply to the three-event sequence of a money-supply increase, an intervening S&P 500 decline, and a later S&P 500 advance.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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All readings on this track · 15 readings
  1. 1987Evaluating weekly price cycles with autocorrelation cutoffs
  2. 1988Serial correlation is not an independence test
  3. 1988Event-triggered chi-square tests for jittered serial links
  4. 1988Reverse the rule before you trust the system
  5. 1990Chi-square evaluation of lagged breadth correlations
  6. 1990Two-gate out-of-sample tests for trading rules
  7. 1990Sign-cell correlation, chi-square checks, and lag shifts
  8. 1998Test serial dependence before you optimize a mechanical system
  9. 2003How a one-rank rotation is constructed for an offset autocorrelation check
  10. 2004Constructing first-order residual autocorrelation tests
  11. 2004A two-stage Durbin-Watson residual screen
  12. 2011Constructing trend labels from increment correlation atoms
  13. 2012Overnight versus daytime return evaluation
  14. 2012Constructing a multi-horizon folded-correlation reversal filter
  15. 2016Tuning indicators to measured market cycles
By fieldStatistical tests95 readingsBy year1988116 readings
All 23 readings tagged Autocorrelation test
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