Optimization {MultiATSM}

Peform the minimization of mean(f)

Description

Peform the minimization of mean(f)

Usage

Optimization(
  f,
  tol,
  varargin,
  FactorLabels,
  Economies,
  ModelType,
  JLLinputs = NULL,
  GVARinputs = NULL
)

Arguments

f

vector-valued objective function (function)

tol

convergence tolerance (scalar). For ML estimation, a reasonable value is tol <- 1e-4

varargin

list containg starting values and constraints: for each input argument K (of f), we need four inputs that look like:

1. a starting value: K0

2. a variable label ('K0') followed by a ':' followed by a type of constraint. The constraint can be:

   • 'bounded': bounded matrix;

   • 'Jordan' or 'Jordan MultiCountry': a matrix of Jordan type;

   • 'psd': psd matrix;

   • 'stationary': largest eigenvalue of the risk-neutral feedback matrix is strictly smaller than 1;

   • 'diag' or 'BlockDiag': a diagonal or block diagonal matrix.

   • 'JLLstructure': to impose the zero-restrictions on the variance-voriance matrix along the lines of the JLL models

3. a lower bound lb (lb <- NULL -> no lower bound)

4. an upper bound ub (ub <- NULL -> no upper bound)

5. Specification of the optimization settings:

   • 'iter off': hide the printouts of the numerical optimization routines;

   • 'fminunc only': only uses fminunc for the optimization;

   • ”fminsearch only': only uses fminsearch for the optimization.

FactorLabels

string-list based which contains the labels of all the variables present in the model

Economies

string-vector containing the names of the economies which are part of the economic system

ModelType

string-vector containing the label of the model to be estimated

JLLinputs

inputs used in the estimation of the JLL-based models; Default is set to NULL

GVARinputs

inputs used in the estimation of the GVAR-based models; Default is set to NULL

Details

If a variable name starts with a '@', it means that that parameter will be analytically concentrated out in the specification of f. In this case, no starting value is needed for this particular parameter (an empty matrix can be provided as a starting value).

Value

(i) out: list of second output produced by f (the first output of f must be the objective value to be minimized).
(ii) x: list containing parameter estimates

References

This function is based on the "LS__opt" 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

Examples

#' # See examples in the vignette file of this package (Section 4).