Transition Matrix of Correlations

[tonino1984]

Homework Statement

Hi all,
I've the following problem: I've a series of correlations matrices, suppose 15x15 matrix of correlations between waves heights. Giving an historical series of correlation values, how can I determine a model to establish that the next correlation matrix has a probabilistic value to be in a determinate state?

Thanks for your help

Homework Equations

The Attempt at a Solution

 

[tonino1984]

Sorry for the bad explanation, I'm trying to do better:
suppose you have a matrix doing like this
(0.2 0.3 0.4)
(0.1 0.1 0.5)
(0.4 0.4 0.1)
at time T0, where at time T1 it changes in
(0.1 0.6 0.2)
(0.4 0.2 0.1)
(0.3 0.2 0.7)

Suppose I've a lot of this hist matrices, how can I determine that probabilisticly the T(n) matrix will be
(0.6 0.7 0.8)
(0.1 0.1 0.5)
(0.4 0.4 0.1)
ie.

Thanks

 

[tonino1984]

Hi there,
any suggestion?

 

[hgfalling]

This seems to be kind of a wide-open question. I mean, do you think that the matrices are dependent on time? Are they dependent on only the matrix from the previous time value? On all the previous matrices?

From a modeling standpoint, it seems like all you have is data. There isn't really a reason to assume a priori that any particular model is right, unless you know something extra about the underlying data. So I think you have to use your knowledge about the particular process here in order to formulate a model to predict T(n).

 

[tonino1984]

This seems to be kind of a wide-open question. I mean, do you think that the matrices are dependent on time? Are they dependent on only the matrix from the previous time value? On all the previous matrices?

From a modeling standpoint, it seems like all you have is data. There isn't really a reason to assume a priori that any particular model is right, unless you know something extra about the underlying data. So I think you have to use your knowledge about the particular process here in order to formulate a model to predict T(n).

Hi hgfalling, thanks for your reply. I've extrapolated several series from those matrix, ie a(1) at T0 then a(1) at T1 etc. to obtain an historical series, and I found that there's a sort of periodical trend in most series, like harmonical series. In fact it's a matrix of waves height, so it's what I supposed to find out. To better understand that model I plot this as "chess board", and I think about this as a set of frames that compose a sort of movie, so I think that every matrix which represents a status is dependent from the previous. In your opinion how can I find out the Tn+1 matrix?

Hope to be more understandable in this tread.

Thx :-)