Inversions and Concordances

日期:2014/03/31

In one's continuing efforts to improve oneself， one read a chapter on quick ways of computing the determinant in chapter 3 of Braun's Differential Equations and Their Application. One never thought he'd have to use determinants again as they had their vogue 60 years ago. However， one came across a curious method which was totally unfamiliar to such as one: "First we pick an element A1j from the first row of the matrix. Then we multiply A1j by an element A2i from the second row of A. However j must not equal i. next we multiply these two numbers by the element in the third row of a in the remaining column". Then you must figure out whether to multiply by +1 or -1 and there you come into the computation of an inversion. An inversion occurs when two pairs in a series are out of order with respect to time and magnitude. See "Kendall's Tau for Serial Dependence".



I believe that the running total of the number of inversions in a time series might be useful for prediction purposes in markets， and I will do some counting now that I am back from California attending the notorious Uncle Howie's 75th birthday. It was a grand birthday with many great handball and paddle ball players in attendance along with a Dr. Harvey Eisenberg， inventor of the total body scan who saved a few lives of the attendees including mine. However， there was one discordant note. Howie is no longer the uncle of legend who will argue with a referee for 20 minutes over a call， and threaten to punch you in the face if you block him out. He has turned mellow in the last 15 years. Everything I wrote about him being the world's best at grabbing defeat at the jaws of victory because of his terrible temper must now be revised and gainsaid.