code

The \solve\code\ subdirectory contains the code for solving the linearized version of a model (solvea.m, solveb.m, checksolve.m, solver.m, qzdiv.m, qzswitch.m).

Additional files used in the examples, but of more general applicability, have been collected here.

For a more complete description of each file, type at the Matlab prompt 'help file'.

bisect	Finds the root of a given function using bisection.
chroot	Checks the accuracy of the feedback part of the solution (matrix A). If A fails the accuracy test, it tries to improve it.	LC
checksolve	Checks the accuracy of the solution matrices A and B.	LC
derivmat	Returns the derivative of row line, line=1,...,M, of (Mx1) function at the point x, and an estimate of the derivative error (in %).	HS-VV
covsp	Computes the covariance matrix C(t)=E[y(t)y(t-t)'] integrating (Gauss-Legendre quadrature) over [-p,p] the spectral density of y(t) = [z(t); x(t)]. z(t) = A z(t-1) + B * s(t) x(t) = G1 * z(t-1) + G2 * s(t) s(t) = P * s(t-1) + e(t), Var(e(t))=Ve It allows HP filtering of y(t).
gauleg	Given the lower and upper limit of integration, this routine returns two vectors containing the abscissas and weights of Gauss-Legendre n-point quadrature formula.
hptrend	Detrends time series with Hodrick-Prescott (HP) filter.	EM
npdf	Computes the pdf of the standard normal distribution.
pentle	Solves a pentadiagonal system of linear equations.	EM
solvea	Computes the feedback part of the policy rule (the matrix A) finding the zero of a matrix polynomial.	LC
qzdiv	Takes upper triangular matrices A, B, orthonormal matrices Q, Z, rearranges them so that all non-zero elements are in lower right corner, while preserving upper triangularity, orthonormal properties and Q'AZ' and Q'BZ'.	CS
qzswitch	Takes upper triangular matrices A, B, orthonormal matrices Q, Z, interchanges diagonal elements i and i+1 of both A and B, while maintaining Q'AZ' and Q'BZ' unchanged.	CS
solveb	Computes the feedforward part of the policy rule (the matrix B) solving a system of linear equations, conditional on A.	LC
solver	Solves for the matrix R used to compute the matrix, B, in the case where there is partial information.	LC
spectral	Gives the spectral denstiy of y(t) = [z(t); x(t)] at frequency w in [-p,p] z(t) = A * z(t-1) + B * s(t) x(t) = G1 * z(t-1) + G2 * s(t) s(t) = P * s(t-1) + e(t), Var(e(t))=Ve
suptitle	Puts a title above all subplots.	DT
trile	Solves a tridiagonal system of linear equations.	EM
tsemat	Finds the Taylor series expansion of a matrix function.	HS-VV