CODEWITHSUNDEEP
matlab
Srishti M
Srishti M

Reputation: 543

Conceptual issues in AR model

I have some basic questions regarding multivariate model. In the ARFIT toolbox, the demo file ardem.m shows the working of a 2nd order bivariate (v1,v2) AR model. The coefficient matrices 

A1 = [ 0.4   1.2;   0.3   0.7 ]
A2 = [ 0.35 -0.3;  -0.4  -0.5 ]

are concatenated into 

A = [ A1 A2 ]

Then a transpose of A is taken. So the result is a 2*4 matrix.

My question is that there should be only 4 coefficients viz. 2 for v1 variable and 2 for v2 variable but why are there 8 coefficients? If the equation format is 

v(k,:) = a11*v1(k-1)+a12*v1(k-2) + a21*v2(k-1)+ a22*v2(k-2)

where a11 = 0.4, a12=1.2, a21=0.3 and a22=0.7.

I think I am missing somewhere in understanding. Can somebody please explain what is the correct representation?

Upvotes: 2

Views: 102

Answers (1)

Buck Thorn
Buck Thorn

Reputation: 5073

The matrices A1 and A2 contain transfer coefficients that describe the contribution of states at times k-1 and k-2, respectively, to the state at time k. Since this is a bivariate process, we are following two variables which can influence each other, and both A1 and A2 are 2 x 2. Writing v1 = v(k,1) and v2 = v(k,2): 

v1(k) = A1(1,1)*v1(k-1) + A1(1,2)*v2(k-1) + A2(1,1)*v1(k-2) + A2(1,2)*v2(k-2)

and similarly for v2(k). Then collectively A1 and A2 contain 8 elements. If the two processes were independent then A1 and A2 would be diagonal and would collectively contain only 4 nonzero elements.

By the way this is not really a Matlab question so I don't think this is the right forum for this question.

Upvotes: 2

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