pseudo.spectrum(mod, ar)
"print"(x, ...)Arima, the fitted model.tsdecARroots returned by roots.allocation.tsdecPSP returned by pseudo.spectrum.print.tsdecPSP containing:
the quotient of the polynomial division (if the degree of the
numerator in the LHS is equal or higher than the degree of the denominator);
the coefficients of total polynomials (numerator and denominator in the LHS)
and the denominators in the RHS.
$$ \sigma^2\frac{\theta(B)\theta(F)}{\phi(B)\phi(F)} = \sigma^2_a\frac{\theta_T(B)\theta_T(F)}{\phi_T(B)\phi_T(F)} + \sigma^2_b\frac{\theta_S(B)\theta_S(F)}{\phi_S(B)\phi_S(F)} + \sigma^2_e \,, $$
where $B$ is the backshift operator and $F=B^(-1)$ is the forward operator. Each term in the right-hand-side is related to the ARIMA models of each one of the unobserved components.
pseudo.spectrum computes the symmetric polynomials of the type
$varphi(B)varphi(F)$ for the polynomials in
the left-hand-side LHS (based on the fitted model) and for the polynomials
in the denominators of the right-hand-side RHS
(based on the allocation of roots of the fitted AR polynomial,
roots.allocation).
Then coefficients in the numerators of the RHS are obtained
by means of partial.fraction .To do so
the terms in the RHS are multiplied by the denominator in the LHS;
then, the coefficients of the numerators in the RHS are obtained
by equating the coefficients of the same order on both sides of
the relationship (the orders of the unknown polynomials are set
to one degree lower than those polynomials of the corresponding denominator).
Hillmer, S. C. and Tiao, G. C. (1982) ‘An ARIMA-Model-Based Approach to Seasonal Adjustment’. Journal of the American Statistical Association, 77(377), pp. 63-70. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.1080/01621459.1982.10477767http://doi.org/10.1080/01621459.1982.10477767doi:\ifelse{latex}{\out{~}}{ }latex~ 10.1080/01621459.1982.10477767
arima, partial.fraction,
roots.allocation.