function a = clmonq(q)
% function a = monq(q)
%  Find the monthly AR coefficient for interpolated data given
%    an estimate of the quarterly AR coefficient
%    Written by E.M. Leeper
%
% First tate the quarterly AR coefficient, q, and then
%     seek the root, a, that solves
%        q = (a^5 + 2 a^4 + 3 a^3 + 2 a^2 + a) / (2 a^2 + 4 a + 3)  (1)

% if n = numerator poly and d = denominator poly in (1)
n = [1 2 3 2 1 0];
d = [2 4 3];
ln = length(n);
ld = length(d);
pad = ln - ld;
dd = [zeros(1,pad) d];
qdd = q.*dd;
newpol = n - qdd;
r = roots(newpol);
for i = 1:length(r)
 if imag(r(i)) == 0
   a = r(i);
 end
end