# Multicountry Term Structure of Interest Rates Models

## Documentation for package ‘MultiATSM’ version 0.2.1

- DESCRIPTION file.
- User guides, package vignettes and other documentation.

## Help Pages

A B C D F G I J K L M N O P R S T U V X Y

## -- A --

A0N_MLEdensity_WOE__jointQ_Bootstrap | Compute the maximum likelihood function (joint Q models) - Bootstrap version
A0N_MLEdensity_WOE__jointQ_sepSigma_Bootstrap | Compute the maximum likelihood function ("joint Q" models for separate Sigma estimation) - Bootstrap version
A0N_MLEdensity_WOE__sepQ_Bootstrap | Compute the maximum likelihood function ("sep Q" models) - Bootstrap version
A0N__computeBnAn_jointQ | Compute the cross-section loadings of yields of a canonical A0_N model ("joint Q" models)
A0N__computeBnAn_sepQ | Compute the cross-section loadings of yields of a canonical A0_N model ("sep Q" models)
aux2true | Map auxiliary (unconstrained) parameters a to constrained parameters b

## -- B --

Bootstrap | Generates the bootstrap-related outputs
BootstrapBoundsSet | Builds the confidence bounds and graphs (Bootstrap set)
bound2x | Transform a number bounded between a lower bound and upper bound to x by:
BR_jps_out | Replications of the JPS (2014) outputs by Bauer and Rudebusch (2017)
BUnspannedAdapJoint | Transform B_spanned into B_unspanned for jointQ models
BUnspannedAdapSep | Transform B_spanned into B_unspanned for sepQ models
BUnspannedAdapSep_BS | Obtain the full form of B unspanned for "sep Q" models within the bootstrap setting

## -- C --

contain | Check whether one element is a subset of another element

## -- D --

DatabasePrep | Prepare the GVARFactors database
DataForEstimation | Retrieve data from Excel and build the database used in the model estimation
DataSet_BS | Prepare the factor set for GVAR models (Bootstrap version)
df__dx | Computes numerical first order derivative of f(x)

## -- F --

FactorsGVAR | Data: Risk Factors for the GVAR - Candelon and Moura (2021)
FEVDandGFEVDbs_jointQ | Creates the confidence bounds and the graphs of FEVDs and GFEVDs after bootstrap ("joint Q" models)
FEVDandGFEVDbs_jointQ_Ortho | Creates the confidence bounds and the graphs of FEVDs and GFEVDs after bootstrap (JLL-based models)
FEVDandGFEVDbs_sepQ | Creates the confidence bounds and the graphs of FEVDs and GFEVDs after bootstrap ("sep Q" models)
FEVDgraphsJLLOrtho | FEVDs graphs for orthogonalized risk factors of JLL-based models
FEVDgraphsJoint | FEVDs graphs for ("joint Q" models)
FEVDgraphsSep | FEVDs graphs for ("sep Q" models)
FEVDjoint | FEVDs for "joint Q" models
FEVDjointOrthogoJLL | Orthogonalized FEVDs for JLL models
FEVDjointOrthogoJLL_BS | FEVDs after bootstrap for JLL-based models
FEVDjoint_BS | FEVDs after bootstrap for "joint Q" models
FEVDsep | FEVDs for "sep Q" models
FEVDsep_BS | FEVDs after bootstrap for "sep Q" models
FitgraphsJoint | Model fit graphs for ("joint Q" models)
FitgraphsSep | Model fit graphs for ("sep Q" models)
FMN__Rotate | Performs state rotations
ForecastYields | Gather bond yields forecasts for all the model types
ForecastYieldsJointQ | Bond yields forecasts ("joint Q" models)
ForecastYieldsSepQ | Bond yields forecasts ("sep Q" models)
Functionf | Set up the vector-valued objective function (Point estimate)
Functionf_Boot | Set up the vector-valued objective function (Bootstrap)
f_with_vectorized_parameters | Use function f to generate the outputs from a ATSM

## -- G --

GaussianDensity | computes the density function of a gaussian process
getpara | Extract the parameter values from varargin
getx | Obtain the auxiliary values corresponding to each parameter, its size and its name
GFEVDgraphsJLLOrtho | GFEVDs graphs for orthogonalized risk factors of JLL-based models
GFEVDgraphsJoint | GFEVDs graphs for ("joint Q" models)
GFEVDgraphsSep | GFEVDs graphs for ("sep Q" models)
GFEVDjoint | GFEVDs for "joint Q" models
GFEVDjointOrthoJLL | Orthogonalized GFEVDs for JLL models
GFEVDjointOrthoJLL_BS | GFEVDs after bootstrap for JLL-based models
GFEVDjoint_BS | GFEVDs after bootstrap for "joint Q" models
GFEVDsep | GFEVDs for "sep Q" models
GFEVDsep_BS | GFEVDs after bootstrap for "sep Q" models
GIRFgraphsJLLOrtho | GIRFs graphs for orthogonalized risk factors of JLL-based models
GIRFgraphsJoint | GIRFs graphs for ("joint Q" models)
GIRFgraphsSep | GIRFs graphs for ("sep Q" models)
GIRFjoint | GIRFs for "joint Q" models
GIRFjointOrthoJLL | Orthogonalized GIRFs for JLL models
GIRFjointOrthoJLL_BS | GIRFs after bootstrap for JLL-based models
GIRFjoint_BS | GIRFs after bootstrap for "joint Q" models
GIRFSep | GIRFs for "sep Q" models
GIRFSep_BS | GIRFs after bootstrap for "sep Q" models
GraphicalOutputs | Generate the graphical outputs for the selected models (Point estimate)
GVAR | Estimate a GVAR(1) and a VARX(1,1,1)

## -- I --

IdxAllSpanned | Find the indexes of the spanned factors
IdxSpanned | Extract the indexes related to the spanned factors in the variance-covariance matrix
InputsForMLEdensity | Generates several inputs that are necessary to build the likelihood function
InputsForMLEdensity_BS | Generates several inputs that are necessary to build the likelihood function - Bootstrap version
InputsForOutputs | Collect the inputs that are used to construct the numerical and the graphical outputs
IRFandGIRFbs_jointQ | Creates the confidence bounds and the graphs of IRFs and GIRFs after bootstrap ("joint Q" models)
IRFandGIRFbs_jointQ_Ortho | Creates the confidence bounds and the graphs of IRFs and GIRFs after bootstrap (JLL-based models)
IRFandGIRFbs_sepQ | Creates the confidence bounds and the graphs of IRFs and GIRFs after bootstrap ("sep Q" models)
IRFgraphsJLLOrtho | IRFs graphs for orthogonalized risk factors of JLL-based models
IRFgraphsJoint | IRFs graphs for ("joint Q" models)
IRFgraphsSep | IRFs graphs for ("sep Q" models)
IRFjoint | IRFs for "joint Q" models
IRFjointOrthoJLL | Orthogonalized IRFs for JLL models
IRFjointOrthoJLL_BS | IRFs after bootstrap for JLL-based models
IRFjoint_BS | IRFs after bootstrap for "joint Q" models
IRFsep | IRFs for "sep Q" models
IRFsep_BS | IRFs after bootstrap for "sep Q" models

## -- J --

JLL | Set of inputs present at JLL's P-dynamics

## -- K --

K1XQStationary | Impose stationarity under the Q-measure
killa | Eliminates the @

## -- L --

LabelsSpanned | Generate the labels of the spanned factors
LabelsStar | Generate the labels of the star variables
LabFac | Generates the labels factors

## -- M --

Maturities | Create a vector of numerical maturities in years
MLEdensity_jointQ | Compute the maximum likelihood function ("joint Q" models)
MLEdensity_jointQ_sepSigma | Compute the maximum likelihood function ("joint Q" models for separate Sigma estimation)
MLEdensity_sepQ | Compute the maximum likelihood function ("sep Q" models)
ModelPara | Replications of the JPS (2014) outputs by the MultiATSM package
MultiATSM | ATSM Package

## -- N --

NumOutputs | Construct the model numerical outputs (model fit, IRFs, GIRFs, FEVDs, and GFEVDs)
NumOutputs_Bootstrap | Numerical outputs (IRFs, GIRFs, FEVD, and GFEVD) for bootstrap

## -- O --

Optimization | Peform the minimization of mean(f)
Optimization_Boot | Peform the minimization of mean(f) (adapted for the bootstrap setting)
OutputConstructionJoint | Numerical outputs (variance explained, model fit, IRFs, GIRFs, FEVDs, and GFEVDs) for "joint Q" models
OutputConstructionJoint_BS | Gathers all the model numerical ouputs after bootstrap for "joint Q" models
OutputConstructionSep | Numerical outputs (variance explained, model fit, IRFs, GIRFs, FEVDs, and GFEVDs) for "sep Q" models
OutputConstructionSep_BS | Gathers all the model numerical ouputs after bootstrap for "sep Q" models

## -- P --

ParaLabels | Create the variable labels used in the estimation
pca_weights_one_country | Weigth matrix from principal components (matrix of eigenvectors)
PdynamicsSet_BS | Compute some key parameters from the P-dynamics (Bootstrap set)
pos2x | Transform a positive number y to back to x by:

## -- R --

Reg_K1Q | Estimate the risk-neutral feedbak matrix K1Q using linear regressions
Reg__OLSconstrained | Restricted OLS regression
RemoveNA | Exclude series that contain NAs
RiskFactors | Data: Risk Factors - Candelon and Moura (2021)
RiskFactorsGraphs | Spanned and unspanned factors plot
RiskFactorsPrep | Builds the complete set of time series of the risk factors (spanned and unspanned)
RMSEjoint | Compute the root mean square error ("joint Q" models)
RMSEsep | Compute the root mean square error ("sep Q" models)

## -- S --

SpannedFactorsjointQ | Gather all spanned factors ("joint Q" models)
SpannedFactorsSepQ | Gather all spanned factors ("sep Q" models)
Spanned_Factors | Compute the country-specific spanned factors
sqrtm_robust | Compute the square root of a matrix
StarFactors | Generates the star variables necessary for the GVAR estimation

## -- T --

TradeFlows | Data: Trade Flows - Candelon and Moura (2021)
Transition_Matrix | Compute the transition matrix required in the estimation of the GVAR model
true2aux | Map constrained parameters b to unconstrained auxiliary parameters a.

## -- U --

update_para | converts the vectorized auxiliary parameter vector x to the parameters that go directly into the likelihood function.

## -- V --

VAR | Estimates a VAR(1)
VarianceExplainedJoint | Percentage explained by the spanned factors of the variations in the set of observed yields for "joint Q" models
VarianceExplainedSep | Percentage explained by the spanned factors of the variations in the set of observed yields for "sep Q" models

## -- X --

x2bound | Transform x to a number bounded btw lb and ub by:
x2pos | Transform x to a positive number by: y = log(e^x + 1)

## -- Y --

Yields | Data: Yields - Candelon and Moura (2021)
YieldsFitJoint | Computes two measures of model fit for bond yields
YieldsFitsep | Computes two measures of model fit for bond yields