markov chain question

George A. Martin (gmartin@econs.umass.edu)
Sat, 31 Jan 1998 16:34:24 -0500 (EST)


Dear Splusers,

I have a basic question that is not so much an Splus question per se, but
is surely within the realm of expertise of members of this list.

Suppose I have sequence of categorical observations on a particular
entity at regularly spaced intervals from which I construct a Markov
transition matrix. Those categories could be, for example, "size",
"shape" and "orientation", with possible states [big, small], [round,
square] and [left, right]; for every time period I would then have a
3-vector of characteristics which would describe the state of the entity.
Thus, in this case I would have a 8 x 8 transition matrix. Suppose
further that for another such entity, I construct a second, and
differing, Markov transition matrix based on observations over the same
categorical state space.

My question, then, is this: what would be an appropriate dimensionless
measure of similarity between these two markov processes? I am
particularly interested in a measure that would be akin to
(contemporaneous) correlation.

Answers, suggestions and references will be much appreciated!

Thanks,

George Martin

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George A. Martin, Research Associate
Center for International Securities and Derivatives Markets
Department of Finance and Operations Management
School of Management
University of Massachusetts
Amherst, MA 01003

phone: (413) 545-3180
fax: (413) 545-3858
e-mail: gmartin@econs.umass.edu
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