Evaluating mechanical trend signals from ten-session average excursions

Audit one mechanical crossing signal

A century of daily industrial-average closes supplied 27,380 sessions and 4,098 crossings of a ten-session average, split evenly into 2,049 upward and 2,049 downward penetrations. The ten-session average is a simple average of the latest ten daily closes, used only as a reference line for signed percentage distance and for counting consecutive closes on one side of that line.

The mechanical crossing signal is a same-side entry cue defined solely by the close moving from one side of the ten-session average to the other, with no discretionary overlay. After each such crossing, the signed excursion is the percentage gap between a daily close and the average during the uninterrupted stay, recorded to a peak distance and a duration in sessions.

Peak distance and time on each side

Across the full sample the mean peak distance above the ten-session average and the mean peak distance below it were both 1.6 percent, while the average stay above the line lasted nearly two sessions longer than the average stay below it.

Mean peak percentage distances in 1901 to 1910 were 1.4 percent above and 1.6 percent below, close to those in 1991 to 2000, which were 1.5 percent above and 1.4 percent below.

How often the next signed excursion continues

After an upward crossing, the series later reached at least 0.5 percent above the average on 74 percent of occasions, or 1,516 signals. After a downward crossing it later reached at least 0.5 percent below on 69 percent of occasions, or 1,414 signals.

A later distance of 1 percent or more from the average occurred on 58 percent of upward crossings and 52 percent of downward crossings. A later distance of 2 percent or more occurred on 30 percent and 29 percent. A later distance of 3 percent or more occurred on 13 percent and 16 percent.

Continuation after threshold is a later close that pushes at least another half percent beyond a pre-chosen two-percent or three-percent distance from the average, counted as further travel rather than as an automatic reversal. Once a plus-2-percent or plus-3-percent distance was first reached, that further half-percent continuation occurred on 65 percent of those episodes. Once a minus-2-percent or minus-3-percent distance was first reached, it occurred on 75 percent and 70 percent of episodes.

Occupying runs and the share of the sample they fill

When a short-term trend was defined as at least ten consecutive closes on one side of the ten-session average, 24 percent of the 4,098 crossings began such an occupying run, including 29 percent of upward crossings and 20 percent of downward crossings. An occupying run separates those longer one-sided phases from the larger set of all crossings.

Those ten-session-or-longer runs accounted for 64 percent of all days spent above the average and 50 percent of all days spent below it, or 58 percent of the 27,380 sessions in the sample.