[R-SIG-Finance] how to enter coefficient matrices of a VAR into dse::ARMA?

Degang WU samuelandjw at gmail.com
Sun Jan 17 16:48:13 CET 2016


Suppose I have a VAR(p) process with known coefficient matrices

y_t = A_1 y_{t-1} + A_2 y_{t-2} + .. A_p y_{t-p} + e_t

where {y_i} are vectors, {A_i} are coefficient matrices and e_t is white noise.

Now I want to enter the coefficient matrices into dse::ARMA.

However, dse::ARMA requires writing the process in the form of 

A(L)y(t) = B(L)w(t) + C(L)u(t) + TREND(t),

where A(L)=I - \sum_i A_i L^i, where L is the lag operator.

I have no idea how to write the lag operator as a numerical matrix.

The documentation of dse::ARMA future states that A is a

(axpxp) is the auto-regressive polynomial array.

which is even more confusing.

The example in the documentation is

AR   <- array(c(1, .5, .3, 0, .2, .1, 0, .2, .05, 1, .5, .3) ,c(3,2,2))
VAR  <- ARMA(A=AR, B=diag(1,2))

However, the example does not mention what the coefficient matrices {A_i} look like in the first place, so it does not help at all.

So my question is, how to write the matrix A dse::ARMA requires in terms of known coefficient matrices {A_i}?

Degang Wu
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