Jan

27

 Since December 19 2011, we've gone through a remarkable bullish period in the market. We had 19 out of 23 days up as of close yesterday. A good way to quantify these is with scans, a variant of runs except instead of x in a row in the same direction, it's x out of the recent y in the same direction. Like runs, scans could be quantified with magnitudes by multiplying the consecutive changes adjusted for mean together and normalizing by a goodmanesque number.

One notes that out of the last 3400 daily trading days from year end 1995 in S&P, such an event occurred just 5 times; all such happened in 2010, around the middle of March, March 12, March 16, March 22, March 23, and Nov 9 (note the failure of independence and thus the need for a real goodmanesque adjustment). One notes that 20 days later they all were up, an average of 3%. Rocky Humbert rules again.

It is interesting to note that there has never been a 19 or 23 down, but there were four, 17 of 23 down, all around Aug 8th, Aug 10, Aug 22, and one outlier 9/29/1999. Anyone who didn't take out the cane during those times, lost a quick 6%. It is interesting to reflect on this phenomenon and to see the "expert " for what he is.

A nice application of scan statistics is contained in Fast Spatial Scan .

A textbook on scans from Wiley is Balakrishnan, N. and Koutras, M. V. (2002): Runs and Scans with Applications.

Also, one notes that bonds have set some nice clusters, with 19 of 23 up occurring 3 times since 1996 being bullish.


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