markov chain question

George A. Martin (
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!


George Martin

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