REPEATING INTERVALS: 
1987 - 1997 & 1997 - 2007

David McMinn

Moon Sun Finance

Amazingly for the US stock market, the intervals between 1987 - 1997 and 1997 - 2007 repeated very closely for the summer highs, the autumn highs, the spring highs and spring lows. From this finding, the 1987 and 1997 October panics looked as though they would also repeat in 2007. This was not to the case. Even so, the 1987 - 1997 and 1997 - 2007 market intervals are presented below for your interest.

Intervals: 1987 - 1997 & 1997 - 2007

Summer Highs in 1987 (Aug 25) and 1997 (Aug 8) were separated by an interval of 3634 days or 123.06 synodic months (equivalent to a Triple Hepton eclipse cycle). Guess what the interval was between the summer highs in 1997 (Aug 8) and 2007 (Jul 19)? Yes you were correct 3634 days.

Autumn Highs. The interval between the DJIA autumn highs in 1987 (Oct 2) and 1997 (Oct 7) was 3658 days. This interval repeated closely (3654 days) between the autumn highs in 1997 (Oct 7) and 2007 (Oct 9).

Spring Highs. The interval between the spring highs in 1987 (Apr 6) and 1997 (May 27) was 3704 days. This compares with the 3705 day interval between the 1997 spring high (May 27) and the 2007 summer high (Jul 19).

Spring Lows. There were 3614 days between the spring lows in 1987 (May 20) and 1997 (Apr 11), which was nearly identical to the 3615 days recorded between the spring lows in 1997 (Apr 11) and 2007 (Mar 5).

The findings have been summarised as follows:

Lows Between The Summer & Autumn Highs. Market lows in 1987 (Sep 21) and 2007 (Aug 16) occurred between the summer highs and the autumn highs. The interval between these two lows was 7269 days, which was almost the same as the 7268 days between the summer highs in 1987 (Aug 25) and 2007 (Jul 19). 

After the summer high in 1997, a low occurred on August 29, which did not fall midway between the corresponding lows in 1987 and 2007. This was unusual given that the other 1987 - 1997 and 1997 - 2007 intervals worked so precisely to within one day. (The ideal date for the anomalous 1997 low would have been September 3, 1997 and thus the actual day was out by four days.)

The interval between the October panics in 1987 and 1997 was 3661 days and, by extrapolation, a panic could have been expected around November 5, 2007. This did not occur. 

Peak – Crash Intervals.

In 1929, 1987, 1997 & 2007, DJIA lows were experienced between 23 and 31 days after the summer record highs. The ensuing autumn highs for 1929, 1987, 1997 and 2007 happened in early October to be followed by a crash two or three weeks later in 1929, 1987 and 1997. The October crash failed to happen in 2007, as expected.

The intervals of 123.0  and 124.0 synodic months were particularly important in the timing of the 1987 & 1997 record peaks, the AOD falls, the AOD rises and the post crash lows. The Triple Hepton of 123 synodic months only appeared between the summer highs in 1997 and 2007.

Conclusions

The hypothesis was that intervals for 1987 - 1997 would repeat for 1997 - 2007, view that held up well for the summer and autumn highs, as well as the spring highs/lows. However, this did not extend for the panic event, as this failed to occur in 2007. How such intervals behave over extended periods remains enigmatic. 

© Copyright 2007. David McMinn. All rights reserved.


References

McMinn, David. Market Timing By The Moon & The Sun. Twin Palms Publishing. 2006 .

Glossary

Apogee is the point in the Moon's orbit greatest distance to the Earth.
Annual One Day rise or fall is the biggest one day % rise or fall in the year commencing March 1.
Ecliptic. The plane of the Earth's orbit around the Sun, which is inclined at 23.5^o to the plane of the Earth's equator.
Equinoxes are node points where the plane of the Earth’s equator cuts the ecliptic. At these points, the equatorial ascending node is where the Sun passes from below to above the celestial equator at 0 E^o (0 Aries - vernal or spring equinox at around 20 March) as viewed from the northern hemisphere. The equatorial descending node is where the Sun passes from above to below the celestial equator at 180 E^o (0 Libra - autumnal equinox at around 22 September).
Full Moon. Occurs when the Earth is positioned between the Sun and Moon (ie: the Moon - Sun angle is 180^o when viewed from Earth).
Inex separates two consecutive Saros series and is equal to 358 synodic months (28.95 tropical years). In the Inex period, the Sun repeats the same angle to the Moon with the north node 180 E^o on the opposite side of the ecliptic.
Lunar day is the period from moonrise to moonrise and equals 24.8412 hours.
Month, Apogee (or Anomalistic Month) is the time taken for the Moon to complete one cycle from perigee to perigee and equals 27.5546 days.
Month, Nodical (or Draconic Month). The time taken for the Moon to complete one cycle north node to north node and is equal to 27.2122 days.
Month, Synodic (or Lunar Month). The time taken for the Moon to complete one cycle new Moon to new Moon and is equal to 29.5306 days.
Month, Tropical. The time taken for the Moon to complete one 360^o cycle of the ecliptical  circle and equals 27.3216 days.
Moon's Orbital Plane. Plane of the Moon's orbit around the Earth, which is inclined by 5^o to the ecliptic plane.
New Moon. Occurs when the Moon passes between the Sun and Earth (ie: the Moon - Sun angle is 0^o when viewed from Earth).
Nutation Cycle. The time taken for the Moon's north node to complete one 360^o cycle retrograde (ie: clockwise) through the ecliptic circle and equals 18.6133 tropical years.
Node. In astronomy, these are two points (eg: equinoxes, lunar nodes, etc) where the orbit of a heavenly body cuts an astronomical plane or where two astronomical planes intersect.
Node, Moon’s. The plane of the Moon's orbit is inclined at 5^o to the plane of the Earth's orbit around the Sun (the ecliptic). The lunar nodes are the points where these two planes intersect. The north or ascending node is where the Moon passes from below to above the ecliptic (South to North). The south or descending  node is where the Moon passes from above to below the ecliptic (North to South).
Nodical Cycles of the Sun and Moon. This covers two lunisolar cycles - the nodical year (Sun angle to the north node ) and the nodical month (Moon angle to the north node).
Perigee. The point in the Moon's orbit closest distance to the Earth. It takes 8.85 years to complete one cycle of the ecliptic circle in direct motion (anticlockwise).
Saros Cycle. This is the interval between two similar eclipses (every 223 lunar months or 6,585.32 days) when the relative angles between the Sun, Moon and Moon’s nodes repeat to within a degree.
Saros Cycle, Triple (or Exeligmos) Because of the extra one-third day in the Saros (6,585.32 days), an eclipse happens every 18.03 years approximately 120^o longitude further West on the surface of the Earth. After three Saros cycles of 54.09 years from the precise date of an eclipse, another occurs at about the same longitude.
Solstice. Times of the year when the Sun is furthest from the equator at 270 E^o (December 22) or 90 E^o (June 21).
Year, Lunar  is the year based on 12 synodic months and it is equal to 354.37 days. This is found in astronomy as the interval between the Saros cycle (223 synodic months) and Metonic cycle (235 synodic months).
Year, Nodical (or Eclipse Year) is the time taken for the Sun to complete one cycle north node to north node and equals 346.6201 days.
Year, Tropical. (or Solar Year) Time taken for the Sun to complete one cycle of the ecliptic circle from spring equinox to spring equinox and is equal to 365.2422 days.

Appendix 1

TRIPLE HEPTON ECLIPSE CYCLE

The Hepton is well established in eclipse cycle theory. This cycle multiplied by three gives the Triple Hepton cycle of about 10 years. as follows: