FMN__Rotate function

Performs state rotations

FMN__Rotate(y0, U1, U0)

Arguments

• y0: list of model parameters as described below
• U1: matrix (N x N)
• U0: vector (N x 1). Optional. Default: vector of zeros.

Returns

y1 - list of outputs after the transformation, the structure parallels that of y0

Details

This function performs a rotation from a model with Z as states to one with S = U0 + U1*Z as states.

Specifically, each model is characterized by the following inputs organized in a list of variables:

(i) K0: intercepts (N x 1);

(ii) K1: feedback matrix (N x N*p);

(iii) SS: volatility matrices (N x N*(M+1))

More specifically, the state Z follows the dynamics:

Z_t = N(K0 + K1 [Z_{t-1}; Z_{t-2}; ...], SSi[ , , 1] + sum_{i=1}^M SSi[ , ,i+1]

where SSi <- array(SS, c(N, N, M+1))

References

#' This function is modified version of the "FMN__Rotate" function by Le and Singleton (2018).

"A Small Package of Matlab Routines for the Estimation of Some Term Structure Models."

(Euro Area Business Cycle Network Training School - Term Structure Modelling). Available at: https://cepr.org/40029