28 May - NYAN

Surfing around the EW-b'osphere, it's easy to find raging debates over how to count recent years' waves.  Bulls versus bears.  Fives versus threes.  Running flats against all comers.  I've found these discussions to be educational, exciting, entertaining, and, perhaps most of all, frustrating.  If you can relate, you are in luck:  I've done it.  I've uncovered the definitive count.  Here it is in all its splendorous glory:

Clearly, these are nyancat waves.  They seemed to go on and on, and on, and nyaon--longer than most anyone expected.  Longer than many people could even handle--they had to turn away.  Nonetheless, there is a rhythm to be found, even if it's not what's considered classical.  At first, translation into a more native language/labeling seems necessary to better understand, but it turns out it's really no help--the meaning is open for debate.  Some argue it isn't real, but it's right there staring back at us.  We don't have any choice but to accept it for what it is, no matter how much some argue it's evidence that machines have taken over for women...


For further emphasis, here's some nyancat-on-nyancat-on-nyancat action:

Nyanyanyanyaynayan!


A note about time relationships:  the two nyancat waves lasted 210 and 88 trading days respectively.


88 is in 1/d_s proportion to 210 with an error of 1 trading day--the ratio is just under 42%.  Since the number of half-trading-days during the 88 day period is a greater percentage of its wave's total than the number of those in the 210 day period, when you look at trading hours, the approximation of d_s improves.

Both 88 and 210 can be represented as sums of a non-repeating subset of the Pell sequence (kind of like a partial sum, but without a requirement of a contiguous range).  The odds of an integer from 1 to 210 having a representation as a sum of a subset of the Pell sequence is a familiar value:  there are 88 of those 210 integers.

In a 1940 essay titled "The Basis of the Wave Principle," RN Elliott analyzed time relationships during a twenty plus year period starting in August 1921.  Through work much more meticulous than what's above, he managed to isolate exactly two waves of Fibonacci duration in years.  There are eight Fibonacci numbers from 1 to 21:  F(1), F(2), F(3), F(4), F(5), F(6), F(7), and F(8).  8/21 = 38%.

In other words, the number of Fibonacci representations of a number within the time period Elliott analyzed is a smaller percentage (less likely, implying more meaningful analytically) than the number of convoluted partial sums of Pell numbers within the length of the largest nyancat wave above.  Note that if the entire period encompassing the nyancat waves were used, the tables turn significantly.  Likewise if the maximum individual size of the Fibonacci duration waves provide basis instead of the entire 20+ year period.  Those asides aside, it can be said that Fibonacci time analysis from Elliott is more unlikely (aka, statistically meaningful) than the Pell time analysis above.  The margin of difference is almost 4%.

For reference here are Elliott's Fibonacci waves and the Pell nyancat waves with durations highlighted (DJIA presented instead of The New York Times 50 stock index Elliott evaluated; the local minima and maxima are qualitatively equivalent for the purposes of the waves in question):

The point of these observations is not to dissuade anyone from the belief that the measure of the duration of the nyancat waves are a numerological oddity.  Rather, I would hope that it does speak to another point:  to dismiss them as such an oddity while maintaining belief in Fibonacci-based financial market time measurements is statistically tenuous.