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One unusually large abnormal return can make a group average look like a common reaction. In his event-study procedure, MacKinlay recommends diagnostics because results from a small set of observations can be heavily influenced by one or two firms. Applying that warning to a Gann-style inspection date is a test-design analogy: the paper studies identifiable events, not a validated calendar cycle. Freeze the date, the five securities, the normal-return baseline, and equal weights before looking at the event bars. Imagine synthetic day-zero abnormal returns of +1%, +1%, +2%, +2%, and +19%. Their mean is +5%. Remove each security in turn only for a sensitivity calculation; the five four-stock means are +6%, +6%, +5.75%, +5.75%, and +1.5%. Deleting the +19% observation shifts the reported mean by 3.5 percentage points, a 70% drop from the full-sample mean. The other deletions change it by no more than one point. Keep the original five-stock mean as the primary result and display the largest leave-one-out change beside it. Do not discard the inconvenient constituent after seeing the data. The diagnostic tells you how fragile a particular average is; it does not reveal which inspection dates deserve to be traded.

Try it

Five hypothetical abnormal returns on a prespecified inspection date are +1%, +1%, +2%, +2%, and +19%. Find the equal-weight mean, all five leave-one-out means, and the largest absolute change from the full mean. What percentage of the full mean is that change?

Limits

These five returns are invented and their normal-return model is not estimated. Leave-one-out is a descriptive sensitivity check, not a significance test. Correlation among stocks and repeated-date selection also matter. MacKinlay does not test Gann dates, and this example offers no market-direction or trading prediction.

Source

A. Craig MacKinlay, Event Studies in Economics and Finance, Section 2, Procedure for an Event Study, printed p. 15, concluding diagnostics paragraph (right column). Peer-reviewed Journal of Economic Literature 35(1), March 1997, pp. 13-39; article reproduced in a public court exhibit. The five-stock Gann-style illustration is synthetic, not a result in the paper.

Mars normally shifts eastward against the background stars in an Earth-centered sky chart. Near the part of its cycle when faster Earth overtakes it, the sightline can sweep backward: Mars appears to move westward for a time even while both planets continue orbiting the Sun in their usual directions. NASA's Mars fact sheet lists sidereal orbital periods of 365.256 days for Earth and 686.980 for Mars, with a mean Earth-Mars synodic period of 779.94 days. The relative beat is approximately one divided by (one over Earth's period minus one over Mars's period). It measures how long before their relative orbital alignment recurs, not the length of an individual retrograde loop. This separates two clocks often mixed in astrology copy. The heliocentric orbit has not reversed; the geocentric apparent longitude can temporarily reverse. A station is a change in the apparent rate's sign, which needs dated positions or an ephemeris rather than the average beat alone. To apply the distinction, write down the coordinate frame, the observation timestamps, and the actual price bar on the same chart before discussing any market proxy. A repeated geometric alignment is an astronomical fact; a repeated return response would require its own test.

Try it

NASA lists Earth and Mars sidereal periods of 365.256 and 686.980 days. Compute the approximate relative alignment period as 1 / (1/365.256 - 1/686.980) days. Does this number give the dates when Mars stations?

Limits

The period calculation uses mean sidereal orbits; orbital eccentricity changes exact geometry. Earth-Mars alignment is not identical to Mars's apparent station, and neither event specifies an asset's direction or volatility. NASA's orbital periods are astronomy, not validation of a trading strategy.

Source

NASA NSSDC, Mars Fact Sheet, Orbital parameters table, rows Sidereal orbit period and Synodic period; NASA Astronomy Picture of the Day, Mars in the Loop, November 8, 2018, for the overtaking explanation. NASA planetary fact sheet and NASA APOD astronomy account. The market-chart protocol and arithmetic exercise are editorial teaching, not NASA market claims.