Abstract
where y(t) is an 
vector of variables and e(t) is an
vector of IID(0,I) disturbances. Under certain conditions,
model (1) has the reduced-form (nonexpectational) VARMA(p,q) solution
The paper obtains the following results for computing
the reduced-form coefficient matrices 
,
, in terms of given
values of the structural coefficient matrices 
, 
. Nonlinear ``AR cross-equation"
restrictions on in terms of given
values of are
derived in the form of a matrix polynomial equation (MPE).
An eigenvalue method is derived for solving the MPE for values of
with prescribed stability properties
(e.g., stationary or least varying). Directly solvable linear ``MA cross-
equation" restrictions on
in terms of given values of and
previously computed values of are derived.
Most applications require to be invertible.
A ``dual" of the AR-eigenvalue method is
described for transforming into
observationally equivalent invertible values, if necessary.
The paper contributes as follows. Unlike Blanchard and Kahn's (1980) widely
used eigenvalue method, the present method doesn't require the sum of leading
coefficient matrices, 
, to be nonsingular and permits
multiple conditioning information sets, from t to t-p. The method is
apparently the first general analytical method for computing a complete
solution of a general EVARMA model, in particular, with a completely
determined and invertible MA part.
By comparison, e.g., while Dagli and Taylor's (1986)
method tolerates a singular , it is numerical,
and Evans and Honkapohja (1986) only ``characterize" the MA part of a
solution. The paper also
provides some insight into ``deeper structural" conditions under which the AR
part of the solution is unique, by studying conditions for singularity
of a derived matrix W.
