Type:	Package
Title:	Multicountry Term Structure of Interest Rates Models
Version:	1.5.0
Date:	2025-10-23
Description:	Package for estimating, analyzing, and forecasting multi-country macro-finance affine term structure models (ATSMs). All setups build on the single-country unspanned macroeconomic risk framework from Joslin, Priebsch, and Singleton (2014, JF) <doi:10.1111/jofi.12131>. Multicountry extensions by Jotikasthira, Le, and Lundblad (2015, JFE) <doi:10.1016/j.jfineco.2014.09.004>, Candelon and Moura (2023, EM) <doi:10.1016/j.econmod.2023.106453>, and Candelon and Moura (2024, JFEC) <doi:10.1093/jjfinec/nbae008> are also available. The package also provides tools for bias correction as in Bauer Rudebusch and Wu (2012, JBES) <doi:10.1080/07350015.2012.693855>, bootstrap analysis, and several graphical/numerical outputs.
License:	GPL-2 | GPL-3
Encoding:	UTF-8
RoxygenNote:	7.2.3
Imports:	cowplot, ggplot2, hablar, magic, pracma
Suggests:	readxl, testthat (≥ 3.0.0), knitr, rmarkdown, bookdown, kableExtra, magrittr
Depends:	R (≥ 4.3.0)
VignetteBuilder:	knitr
URL:	https://github.com/rubensmoura87/MultiATSM, https://rubensmoura87.github.io/MultiATSM/
BugReports:	https://github.com/rubensmoura87/MultiATSM/issues
NeedsCompilation:	no
Packaged:	2025-10-23 04:00:28 UTC; rmoura
Author:	Rubens Moura [aut, cre]
Maintainer:	Rubens Moura <rubens.gtmoura@gmail.com>
Repository:	CRAN
Date/Publication:	2025-10-23 10:40:26 UTC
Config/testthat/edition:	3
LazyData:	true

ATSM Package

Description

Estimation of several classes of affine term structure of interest rates models.

Author(s)

Rubens Moura rubens.gtmoura@gmail.com

Gathers the estimate of the bootstrap draws

Description

Gathers the estimate of the bootstrap draws

Usage

AdjustOptm_BS(ModelType, ModelBootstrap, Draw_Opt, Economies, tt)

Arguments

Generate paths to save IRFs/GIRFs graphs

Description

Generate paths to save IRFs/GIRFs graphs

Usage

AdjustPathFEVDs(OutputType, ElementType, PathsGraphs, Economies, ModelType)

Arguments

Generate paths to save IRFs/GIRFs graphs

Description

Generate paths to save IRFs/GIRFs graphs

Usage

AdjustPathIRFs(OutputType, ElementType, PathsGraphs, Economies, ModelType)

Arguments

Makes sure that the time series of yields and risk factors have coincident sample spans

Description

Makes sure that the time series of yields and risk factors have coincident sample spans

Usage

AdjustYieldsDates(Yields, PdynamicsFactors, Economies)

Arguments

Adjust the constant label

Description

Adjust the constant label

Usage

Adjust_Const_Type(Const_Type_Full)

Arguments

Transformation of the block diagonal parameters (auxiliary form)

Description

Transformation of the block diagonal parameters (auxiliary form)

Usage

Aux_BlockDiag(ParaValue, Const_Type, FactorLabels, Economies)

Arguments

Transformation of the JLL-related parameters (auxiliary form)

Description

Transformation of the JLL-related parameters (auxiliary form)

Usage

Aux_JLLstruct(ParaValue, Const_Type, FactorLabels, Economies, JLLinputs)

Arguments

Transformation of the Jordan-related parameters (auxiliary form)

Description

Transformation of the Jordan-related parameters (auxiliary form)

Usage

Aux_Jordan(ParaValue, Const_Type, FactorLabels, Economies, JLLinputs)

Arguments

Transformation of a PSD matrix (auxiliary form)

Description

Transformation of a PSD matrix (auxiliary form)

Usage

Aux_PSD(ParaValue, Const_Type)

Arguments

Auxiliary function for a single-country specification

Description

Auxiliary function for a single-country specification

Usage

Aux_jordan_OneCountry(ParaValue, Const_Type)

Arguments

References

Le, A., & Singleton, K. J. (2018). Small Package of Matlab Routines for Estimation of Some Term Structure Models. EABCN Training School.
This function offers an independent R implementation that is informed by the conceptual framework outlined in Le and Singleton (2018), but adapted to the present modeling context.

Replications of the JPS (2014) outputs by Bauer and Rudebusch (2017)

Description

Unspanned macro risk model outputs by Bauer and Rudebusch (2017)

Usage

data("BR_jps_out")

Format

Unspanned macro risk model outputs by Bauer and Rudebusch (2017)

est.llk

summary list of log-likelihood estimations

M.o

time series of unspanned factors

pars

additional summary list of log-likelihood estimations

W

Weight matrix that results from principal components analysis

Y

time series of bond yields

N

total number of risk factor of the model (spanned and unspanned)

R

total number of spanned factor of the model

References

Bauer, M. and Rudebusch, G. "Resolving the Spanning Puzzle in Macro-Finance Term Structure Models"

Transform B_spanned into B_unspanned for jointQ models

Description

Transform B_spanned into B_unspanned for jointQ models

Usage

BUnspannedAdapJoint(G, M, N, C, J, BSpanned)

Arguments

Transform B_spanned into B_unspanned for sepQ models

Description

Transform B_spanned into B_unspanned for sepQ models

Usage

BUnspannedAdapSep(G, M, ModelPara_Short, Economies, Economy, ModelType)

Arguments

Obtain the full form of B unspanned for "sep Q" models within the bootstrap setting

Description

Obtain the full form of B unspanned for "sep Q" models within the bootstrap setting

Usage

BUnspannedAdapSep_BS(G, M, ModelParaBoot, Economies, Economy, ModelType, tt)

Arguments

Estimates an unbiased VAR(1) using stochastic approximation (Bauer, Rudebusch and Wu, 2012)

Description

Estimates an unbiased VAR(1) using stochastic approximation (Bauer, Rudebusch and Wu, 2012)

Usage

Bias_Correc_VAR(
  ModelType,
  BRWinputs,
  RiskFactors,
  Economies,
  FactorLabels,
  GVARinputs = NULL,
  JLLinputs = NULL,
  verbose = TRUE
)

Arguments

Value

Bias-corrected VAR parameters based on the framework of Bauer, Rudebusch and Wu (2012). The list contains:

1. KOZ_BC: estimated intercept (K x 1);

2. K1Z_BC: estimated feedback matrix (K x K);

3. SSZ_BC: estimated variance-covariance matrix (K x K);

4. dist: root mean square distance (scalar);

General Notation

• Td denotes the model time series dimension.

• C number of countries in the system.

• K denotes the total number of risk factors.

References

Bauer, Rudebusch and, Wu (2012). "Correcting Estimation Bias in Dynamic Term Structure Models"
This function offers an independent R implementation that is informed by the conceptual framework outlined in Bauer, Rudebusch and Wu (2012), but adapted to the present modeling context. Related Matlab routines are available on Cynthia Wu's website (https://sites.google.com/view/jingcynthiawu/).

Examples

data(RiskFacFull)
Factors <- t(RiskFacFull[1:7, ])

BRWinputs <- list(
  Cent_Measure = "Mean", gamma = 0.4, N_iter = 1000, N_burn = 100,
  B = 10, check = 1, B_check = 5000
)

Economies <- "China"
N <- 3
ModelType <- "JPS original"
FactorLabels <- NULL

BRWpara <- Bias_Correc_VAR(ModelType, BRWinputs, Factors, Economies, FactorLabels, verbose = FALSE)

Generates the desired bootstrap graphs

Description

Generates the desired bootstrap graphs

Usage

Boot_DataGraphFact_perShock(
  NumOutBounds,
  NumOutPE,
  IdxShock,
  nmResponse,
  Lab_Int,
  ModelType,
  FacDim,
  Horiz,
  Economies = NULL,
  Ortho = FALSE
)

Arguments

Generates the desired bootstrap graphs

Description

Generates the desired bootstrap graphs

Usage

Boot_DataGraphYield_perShock(
  NumOutBounds,
  NumOutPE,
  IdxShock,
  nmResponse,
  Lab_Int,
  ModelType,
  FacDim,
  YieldDim,
  Horiz,
  Economies = NULL,
  Ortho = FALSE
)

Arguments

Build P-dynamic graphs after the bootstrap implementation

Description

Build P-dynamic graphs after the bootstrap implementation

Usage

Boot_Fac_Graphs(
  NumOutBounds,
  NumOutPE,
  ModelType,
  FacDim,
  Horiz,
  Economies,
  PathsGraphs,
  OutInt,
  Folder2save,
  WishFacGraphs,
  WishFacGraphsOrtho = NULL
)

Arguments

Build P-dynamic graphs after the bootstrap implementation

Description

Build P-dynamic graphs after the bootstrap implementation

Usage

Boot_Yields_Graphs(
  NumOutBounds,
  NumOutPE,
  ModelType,
  FacDim,
  YielDim,
  Horiz,
  Economies,
  PathsGraphs,
  OutInt,
  Folder2save,
  WishYieldGraphs,
  WishYieldGraphsOrtho = NULL
)

Arguments

Builds template from bootstrap-related graphs

Description

Builds template from bootstrap-related graphs

Usage

Boot_graph_template(ALLdata, nmResponse)

Arguments

Generates the bootstrap-related outputs

Description

Generates the bootstrap-related outputs

Usage

Bootstrap(
  ModelType,
  ModelParaPE,
  NumOutPE,
  Economies,
  InputsForOutputs,
  FactorLabels,
  JLLlist,
  GVARlist,
  WishBC = FALSE,
  BRWlist = NULL,
  Folder2save = NULL,
  verbose = TRUE
)

Arguments

Value

An object of class 'ATSMModelBoot' containing:

• List of model parameters for each draw

• List of numerical outputs (IRFs, GIRFs, FEVDs, GFEVDs) for each draw

• Confidence bounds for the chosen level of significance

Permissible options - Bootstrap list in InputsForOutputs

• methodBS : "bs" (standard bootstrap), "wild" (wild bootstrap), "block" (block bootstrap)

• BlockLength : required input for the block bootstrap method. Block length must be larger than 0 and smallar than the model time series dimension (Td).

• ndraws: number of draws. Must be a positive integer.

• pctg : confidence level. Must be a positive integer. Common choices are: 68, 90 and 95.

Available methods

- autoplot(object, NumOutPE, type)

Examples

data("ParaSetEx")
data("InpForOutEx")
data("NumOutEx")
ModelType <- "JPS original"
Economy <- "Brazil"
FacLab <- LabFac(N = 1, DomVar = "Eco_Act", GlobalVar = "Gl_Eco_Act", Economy, ModelType)

# Adjust Forecasting setting
InpForOutEx[[ModelType]]$Bootstrap <- list(
  WishBootstrap = 1, methodBS = "bs", BlockLength = 4,
  ndraws = 5, pctg = 95
)

Boot <- Bootstrap(ModelType, ParaSetEx, NumOutEx, Economy, InpForOutEx, FacLab,
  JLLlist = NULL,
  GVARlist = NULL, WishBC = FALSE, BRWlist = NULL, Folder2save = NULL, verbose = FALSE
)

Builds the confidence bounds and graphs (Bootstrap set)

Description

Builds the confidence bounds and graphs (Bootstrap set)

Usage

BootstrapBoundsSet(
  ModelType,
  ModelBootstrap,
  NumOutPE,
  InputsForOutputs,
  Economies,
  Folder2save,
  verbose
)

Arguments

Builds the time series of the risk factors that are used in the estimation of the ATSM

Description

Builds the time series of the risk factors that are used in the estimation of the ATSM

Usage

BuildATSM_RiskFactors(
  InitialSampleDate,
  FinalSampleDate,
  Yields,
  GlobalMacroFactors,
  DomMacroFactors,
  Economies,
  FactorLabels,
  ModelType,
  BS_Adj = FALSE
)

Arguments

Value

Generates the complete set of risk factors that are used in the estimation of the ATSM

Build Confidence intervals for yield-related outputs

Description

Build Confidence intervals for yield-related outputs

Usage

BuildCI_Yields(
  NumOutBounds,
  NumOutPE,
  Lab_Int,
  ModelType,
  Economies,
  IdxResp,
  IdxShock,
  Ortho = FALSE
)

Arguments

Build the list of IRF and GIRF for both factors and bond yields

Description

Build the list of IRF and GIRF for both factors and bond yields

Usage

BuildFEVDlist(
  NumOut,
  Economies,
  ModelType,
  FEVDhoriz,
  FacDim,
  YieldsDim,
  OutputType
)

Arguments

Build the GVAR(1) from the country-specific VARX(1,1,1)

Description

Build the GVAR(1) from the country-specific VARX(1,1,1)

Usage

BuildGVAR(ParaVARX, GlobalPara, GVARinputs, DomLabels, GlobalLabels, N)

Arguments

Build the list of IRF and GIRF for both factors and bond yields

Description

Build the list of IRF and GIRF for both factors and bond yields

Usage

BuildIRFlist(NumOut, Economies, ModelType, IRFhoriz, FacDim, OutputType)

Arguments

Build country-specific link matrices

Description

Build country-specific link matrices

Usage

BuildLinkMat(GVARinputs, N, M)

Arguments

Build the time-series of the risk factors in each bootstrap draw

Description

Build the time-series of the risk factors in each bootstrap draw

Usage

BuildRiskFactors_BS(
  ModelParaPE,
  residPdynOriginal,
  residYieOriginal,
  InputsForOutputs,
  Economies,
  ModelType,
  FactorLabels,
  GVARlist,
  JLLlist,
  WishBRW,
  BRWlist,
  nlag = 1,
  verbose
)

Arguments

Build the time-series of bond yields for each bootstrap draw

Description

Build the time-series of bond yields for each bootstrap draw

Usage

BuildYields_BS(
  ModelParaPE,
  ModelType,
  RiskFactors_BS,
  BFull,
  BS_Set,
  Economies
)

Arguments

Input validation for the 'FeedMat_Q' function

Description

Input validation for the 'FeedMat_Q' function

Usage

CheckInput_K1X(Yields, mat_vec, time_step)

Arguments

Check consistence of inputs

Description

Check consistence of inputs

Usage

CheckInputsForMLE(
  t0,
  tF,
  Economies,
  DomesticMacroFac,
  GlobalMacroFac,
  UnitYields,
  DataFreq,
  Label_Single_Models,
  Label_Multi_Models,
  FactorLabels,
  GVARlist,
  ModelType
)

Arguments

Check consistency of the inputs provided in GVARinputs

Description

Check consistency of the inputs provided in GVARinputs

Usage

CheckInputsGVAR(GVARinputs, N)

Arguments

Check consistency of the inputs provided in JLL-based models

Description

Check consistency of the inputs provided in JLL-based models

Usage

CheckJLLinputs(RiskFactorsNonOrtho, JLLinputs)

Arguments

Check Numerical Precision Issues of K1_root matrix

Description

Check Numerical Precision Issues of K1_root matrix

Usage

CheckNumericalPrecision(matrix_in, tolerance = 1e-10)

Arguments

Value

List with precision indicators

check how close the mean or median of the bias-corrected aproach is from the non-corrected approach

Description

check how close the mean or median of the bias-corrected aproach is from the non-corrected approach

Usage

Check_comparison_NoBC(
  K1Z_BC,
  K1Z_NoBC,
  B_check,
  RiskFactors,
  GVARinputs,
  JLLinputs,
  FactorLabels,
  Economies,
  ModelType,
  Use_Mean,
  verbose
)

Arguments

Check consistency of labels (economies, domestic and global variables)

Description

Check consistency of labels (economies, domestic and global variables)

Usage

Check_label_consistency(
  Economies,
  DomesticMacroFac,
  GlobalMacroFac,
  DomVarLab,
  GloVarLab
)

Arguments

Preliminary checks for inputs provided for the performing out-of-sample forecasting

Description

Preliminary checks for inputs provided for the performing out-of-sample forecasting

Usage

ChecksOOS(t0Forecast, t0Sample, nForecasts, ForecastType, TimeLength)

Arguments

Impose the zero-restrictions on the Cholesky-factorization from JLL-based models.

Description

Impose the zero-restrictions on the Cholesky-factorization from JLL-based models.

Usage

CholRestrictionsJLL(SigmaUnres, M, G, N, Economies, DomUnit)

Arguments

Value

restricted version the Cholesky factorization matrix from JLL-based models (K x K)

Clean unnecessary outputs of JLL models in the bootstrap setup

Description

Clean unnecessary outputs of JLL models in the bootstrap setup

Usage

CleanOrthoJLL_Boot(ModelBootstrap, ndraws, ModelType)

Arguments

Compute the confidence bounds around the P-dynamics and bond yields for FEVD and GFEVD

Description

Compute the confidence bounds around the P-dynamics and bond yields for FEVD and GFEVD

Usage

ComputeBounds_FEVDandGFEVD(
  ModelBootstrap,
  quants,
  FacDim,
  YieDim,
  ModelType,
  Economies,
  ndraws,
  Horiz
)

Arguments

Compute the confidence bounds from the model's numerical outputs

Description

Compute the confidence bounds from the model's numerical outputs

Usage

ComputeBounds_IRFandGIRF(
  ModelBootstrap,
  quants,
  FacDim,
  YieDim,
  ModelType,
  Economies,
  ndraws,
  Horiz
)

Arguments

Compute FEVDs for all models

Description

Compute FEVDs for all models

Usage

ComputeFEVDs(
  SIGMA,
  K1Z,
  G0,
  BLoad,
  FactorLabels,
  FacDim,
  MatLength,
  FEVDhoriz,
  YieldsLabel,
  ModelType,
  Economy = NULL,
  CholFac_JLL = NULL,
  PI = NULL,
  Mode = FALSE
)

Arguments

References

• This function is a modified and extended version of the "fevd" function from Smith, L.V. and A. Galesi (2014). GVAR Toolbox 2.0, available at https://sites.google.com/site/gvarmodelling/gvar-toolbox.

• Pesaran and Shin, 1998. "Generalized impulse response analysis in linear multivariate models" (Economics Letters)

Compute GFEVDs for all models

Description

Compute GFEVDs for all models

Usage

ComputeGFEVDs(
  SIGMA,
  K1Z,
  G0,
  BLoad,
  FactorLabels,
  FacDim,
  MatLength,
  GFEVDhoriz,
  YieldsLabel,
  ModelType,
  Economy,
  PI = NULL,
  Mode = FALSE
)

Arguments

References

• This function is a modified and extended version of the "fevd" function from Smith, L.V. and A. Galesi (2014). GVAR Toolbox 2.0, available at https://sites.google.com/site/gvarmodelling/gvar-toolbox.

• Pesaran and Shin, 1998. "Generalized impulse response analysis in linear multivariate models" (Economics Letters)

Compute GIRFs for all models

Description

Compute GIRFs for all models

Usage

ComputeGIRFs(
  Sigma.y,
  F1,
  BLoad,
  G0.y,
  FactorLabels,
  FacDim,
  MatLength,
  GIRFhoriz,
  YieldsLabel,
  ModelType,
  Economy = NULL,
  PI = NULL,
  Mode = FALSE
)

Arguments

Compute IRFs of all models

Description

Compute IRFs of all models

Usage

ComputeIRFs(
  SIGMA,
  K1Z,
  BLoad,
  FactorLabels,
  FacDim,
  MatLength,
  IRFhoriz,
  YieldsLabel,
  ModelType,
  Economy = NULL,
  PI = NULL,
  Mode = FALSE
)

Arguments

Compute the latent loading AnX and BnX

Description

Compute the latent loading AnX and BnX

Usage

Compute_BnX_AnX(mat, N, K1XQ, r0, dX, SSX, Economies, ModelType, Lab_SingleQ)

Arguments

Compute the expected component for all models

Description

Compute the expected component for all models

Usage

Compute_EP(
  ModelPara,
  ModelType,
  UnitYields,
  matAdjUnit,
  N,
  rhoList,
  Economies,
  FactorLabels,
  WishFP = FALSE,
  matMIN = FALSE,
  matMAX = FALSE
)

Arguments

Retrieves data from Excel and builds the database used in the model estimation

Description

Retrieves data from Excel and builds the database used in the model estimation

Usage

DataForEstimation(
  t0,
  tF,
  Economies,
  N,
  FactorLabels,
  ModelType,
  DataFrequency,
  Macro_FullData,
  Yields_FullData,
  DataConnect = NULL,
  W_type = NULL,
  t_First_Wgvar = NULL,
  t_Last_Wgvar = NULL
)

Arguments

Value

A list containing:

1. Yields: matrix (J x Td or CJ x Td) of bond yields for all countries.

2. RiskFactors: matrix (K x Td) of risk factors for all countries.

3. GVARFactors: list of variables used in VARX estimation (see GVARFactors data file). NULL if not GVAR-based.

General Notation

• Td: model time series dimension.

• C: number of countries in the system.

• N: number of country-specific spanned factors.

• K: total number of risk factors.

• J: number of bond yields per country used in estimation.

See Also

Load_Excel_Data

Examples

DomVar <- c("Eco_Act", "Inflation")
GlobalVar <- c("GBC", "CPI_OECD")
t0 <- "2006-09-01"
tF <- "2019-01-01"
Economies <- c("China", "Brazil", "Mexico", "Uruguay", "Russia")
N <- 2
ModelType <- "JPS original"
FactorLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)
DataFrequency <- "Monthly"
MacroData <- Load_Excel_Data(system.file("extdata", "MacroData.xlsx", package = "MultiATSM"))
YieldData <- Load_Excel_Data(system.file("extdata", "YieldsData.xlsx", package = "MultiATSM"))
DataModel <- DataForEstimation(
  t0, tF, Economies, N, FactorLabels, ModelType, DataFrequency,
  MacroData, YieldData
)

Prepare the factor set for GVAR models (Bootstrap version)

Description

Prepare the factor set for GVAR models (Bootstrap version)

Usage

DataSet_BS(ModelType, RiskFactors, Wgvar, Economies, FactorLabels)

Arguments

Value

A list containing the factor set for GVAR models.

Gather data of several countries in a list. Particularly useful for GVAR-based setups (Compute "GVARFactors")

Description

Gather data of several countries in a list. Particularly useful for GVAR-based setups (Compute "GVARFactors")

Usage

DatabasePrep(
  t_First,
  t_Last,
  Economies,
  N,
  FactorLabels,
  ModelType,
  Macro_FullData,
  Yields_FullData,
  Wgvar = NULL
)

Arguments

Value

List containing the risk factor set for all countries and global factors. Particularly useful for GVAR-based models.

General Notation

• C: number of countries in the system.

• N: number of country-specific spanned factors.

Examples

# Load data from excel
macro_data <- Load_Excel_Data(system.file("extdata", "MacroData.xlsx", package = "MultiATSM"))
yields_data <- Load_Excel_Data(system.file("extdata", "YieldsData.xlsx", package = "MultiATSM"))
trade_data <- Load_Excel_Data(system.file("extdata", "TradeData.xlsx", package = "MultiATSM"))

# Adjust trade data
trade_data <- lapply(trade_data, function(df) {
  countries <- df[[1]]
  df <- as.data.frame(df[-1])
  rownames(df) <- countries
  df
})

# Define features of interest
ModelType <- "GVAR multi"
Economies <- c("China", "Uruguay", "Russia")
GlobalVar <- c("GBC", "CPI_OECD")
DomVar <- c("Eco_Act", "Inflation")
N <- 3
t0 <- "2006-09-01"
tF <- "2019-01-01"


# Compute some inputs
FactorLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)
Wgvar <- Transition_Matrix(
  t_First = "2006", t_Last = "2019", Economies,
  type = "Sample Mean", trade_data
)

# Compute GVARFactors
GVARFactors <- DatabasePrep(
  t0, tF, Economies, N, FactorLabels, ModelType, macro_data,
  yields_data, Wgvar
)

Data: domestic risk factors - Candelon and Moura (2024, JFEC)

Description

Domestic risk factors data used in Candelon and Moura (2024, JFEC)

Usage

data("DomMacro")

Format

A matrix of country-specific risk factors (inflation and economic activity growth) for Brazil, China, Mexico, and Uruguay. The data have monthly frequency and span the period from June/2004 to January/2020.

Source

Inflation

year-over-year variation from Consumer price index published by the International Monetary Fund <https://data.imf.org/en/datasets/IMF.STA:CPI>

Eonomic activity

GDP leading indicator published by the OECD <https://www.oecd.org/en/data/indicators/composite-leading-indicator-cli.html>

References

Candelon, B. and Moura, R. (2024) "A Multicountry Model of the Term Structures of Interest Rates with a GVAR". (Journal of Financial Econometrics)

Data: Risk Factors for the GVAR - Candelon and Moura (2023)

Description

Domestic risk factors data used in the GVAR models - Candelon and Moura (2023)

Usage

data("DomMacro_covid")

Format

A matrix of country-specific risk factors (inflation, output growth, CDS, and COVID-19 reproduction rate) for Brazil, India, Mexico, and Russia. The data have weekly frequency and span the period from March 22, 2020, to September 26, 2021.

Source

Inflation

Monthly CPI (from OECD) interpolated to daily data (spline), converted to weekly year-over-year changes, and detrended <https://www.oecd.org/en/data/indicators/inflation-cpi.html>

Output growth

Detrended weekly estimate of GDP year-over-year growth derived from the OECD Weekly Tracker index <https://web-archive.oecd.org/sections/weekly-tracker-of-gdp-growth/index.htm>

CDS

5-year maturity CDS. Simulated data constructed using Bloomberg bond yield series.

COVID-19 reproduction rate

detrended R rate from the Our World in Data database <https://ourworldindata.org/coronavirus>

References

Candelon, B. and Moura, R. (2023) "Sovereign yield curves and the COVID-19 in emerging markets". (Economic Modelling)

Estimate K1h

Description

Estimate K1h

Usage

Est_K1h(horiz, min_mat, max_mat, time_step, B_coef)

Arguments

Estimate a restricted OLS model

Description

Estimate a restricted OLS model

Usage

Est_RestOLS(LHS, RHS, Rmat)

Arguments

Value

matrix of coefficient (M x N)

Estimate numerically the variance-covariance matrix from the GVAR-based models

Description

Estimate numerically the variance-covariance matrix from the GVAR-based models

Usage

EstimationSigma_GVARrest(SigmaUnres, res, IdxVarRest)

Arguments

Value

restricted version of the variance-covariance matrix a GVAR model (K x K)

Estimate numerically the Cholesky-factorization from the JLL-based models

Description

Estimate numerically the Cholesky-factorization from the JLL-based models

Usage

EstimationSigma_Ye(SigmaUnres, res, M, G, Economies, DomUnit)

Arguments

Value

Cholesky-factorization after the maximization (K x K)

Get the expected component of all models

Description

Get the expected component of all models

Usage

ExpectedComponent(
  ModelPara,
  InputsForOutputs,
  ModelType,
  Economies,
  FactorLabels,
  WishFP = FALSE
)

Arguments

FEVDs and GFEVDs for all models

Description

FEVDs and GFEVDs for all models

Usage

FEVDandGFEVD(ModelType, ModelPara, FEVDhoriz, FactorLabels, Economies)

Arguments

Details

Structural shocks are identified via Cholesky decomposition

FEVDs and GFEVDs after bootstrap for all models

Description

FEVDs and GFEVDs after bootstrap for all models

Usage

FEVDandGFEVD_BS(ModelType, ModelParaBoot, FEVDhoriz, FactorLabels, Economies)

Arguments

Creates the confidence bounds and the graphs of FEVDs and GFEVDs after bootstrap (all models)

Description

Creates the confidence bounds and the graphs of FEVDs and GFEVDs after bootstrap (all models)

Usage

FEVDandGFEVDbs(
  ModelType,
  ModelBootstrap,
  NumOutPE,
  InputsForOutputs,
  Economies,
  PathsGraphs,
  Folder2save,
  verbose
)

Arguments

FEVD and GFEVD graphs for all models

Description

FEVD and GFEVD graphs for all models

Usage

FEVDandGFEVDgraphs(
  ModelType,
  NumOut,
  WishPdynamicsgraphs,
  WishYieldsgraphs,
  FEVDhoriz,
  PathsGraphs,
  OutputType,
  Economies,
  Folder2save,
  verbose
)

Arguments

Available Methods

- 'autoplot(object, type = "FEVD_Factor")', 'autoplot(object, type = "FEVD_Yields")', 'autoplot(object, type = "GFEVD_Yields")', 'autoplot(object, type = "GFEVD_Yields")'. For JLL-based models: 'autoplot(object, type = "FEVD_Factor-_Ortho")',
'autoplot(object, type = "FEVD_Yields_Ortho")', 'autoplot(object, type = "GFEVD_Yields_Ortho")', 'autoplot(object, type = "GFEVD_Yields_Ortho")'.

Examples

data("NumOutEx")
ModelType <- "JPS original"
Economy <- "Brazil"
FEVDhoriz <- 20
FEVDandGFEVDgraphs(ModelType, NumOutEx,
  WishPdynamicsgraphs = FALSE, WishYieldsgraphs = TRUE, FEVDhoriz,
  PathsGraphs = NULL, OutputType = "FEVD", Economy,
  Folder2save = NULL, verbose = FALSE
)

Generates graphs for FEVDs and GFEVDs

Description

Generates graphs for FEVDs and GFEVDs

Usage

FEVDandGFEVDs_Graphs(OutputType, FEVDlist, nmVarInt, Lab_Fac, PathsGraphs)

Arguments

Compute quantiles for model P-dynamics

Description

Compute quantiles for model P-dynamics

Usage

FacQuantile_bs(
  DrawSet,
  LabIRF,
  ndraws,
  quants,
  Horiz,
  FacDim,
  DimLabelsFac,
  ModelType,
  Ortho = FALSE
)

Arguments

Compute the confidence bounds for the model bond P-dynamics-related outputs

Description

Compute the confidence bounds for the model bond P-dynamics-related outputs

Usage

FactorBounds_FEVDandGFEVD(
  ModelBootstrap,
  quants,
  ModelType,
  ndraws,
  Horiz,
  FacDim,
  LabFEVD,
  Economies
)

Arguments

Compute the confidence bounds for the model P-dynamics

Description

Compute the confidence bounds for the model P-dynamics

Usage

FactorBounds_IRFandGIRF(
  ModelBootstrap,
  quants,
  ModelType,
  ndraws,
  Horiz,
  FacDim,
  LabIRF,
  Economies
)

Arguments

Makes the pre-allocation of the factors set for JLL-based models

Description

Makes the pre-allocation of the factors set for JLL-based models

Usage

Factors_NonOrtho(NonOrthoFactors, JLLinputs, FactorLab, N)

Arguments

Computes an average or median feedback matrix across several bootstrap iterations

Description

Computes an average or median feedback matrix across several bootstrap iterations

Usage

FeedMat_M(
  K1Z_j,
  N_boot,
  RiskFactors,
  GVARinputs,
  JLLinputs,
  FactorLabels,
  Economies,
  ModelType,
  Use_Mean
)

Arguments

Get an estimate for the risk-neutral (Q) feedback matrix

Description

Get an estimate for the risk-neutral (Q) feedback matrix

Usage

FeedMat_Q(
  Yields,
  Spa_Fac,
  Economies,
  UnitYields,
  time_step,
  check_inputs = TRUE
)

Arguments

References

Le, A., & Singleton, K. J. (2018). Small Package of Matlab Routines for Estimation of Some Term Structure Models. EABCN Training School.
This function offers an independent R implementation that is informed by the conceptual framework outlined in Le and Singleton (2018), but adapted to the present modeling context.

Compute the Feedback matrix of each bootstrap draw

Description

Compute the Feedback matrix of each bootstrap draw

Usage

FeedbackMat_BS(
  ModelType,
  RiskFactors_TS,
  FactorLabels,
  Economies,
  GVARlist,
  JLLlist,
  WishBRW,
  BRWlist,
  verbose
)

Arguments

Set the zero-restrictions on the feedback matrix of JLL's P-dynamics

Description

Set the zero-restrictions on the feedback matrix of JLL's P-dynamics

Usage

FeedbackMatrixRestrictionsJLL(DomUnit, K, G, M, N)

Arguments

Value

matrix containing the restrictions of the feedback matrix (K x K)

Build subplot for fitted yields

Description

Build subplot for fitted yields

Usage

Fit_Subplot(
  YieldData,
  ModelFit,
  ModelImplied,
  MatLength,
  mat,
  Economies,
  ModelType,
  PathsGraphs
)

Arguments

Model fit graphs for all models

Description

Model fit graphs for all models

Usage

Fitgraphs(
  ModelType,
  WishFitgraphs,
  ModelPara,
  NumOut,
  Economies,
  PathsGraphs,
  Folder2save,
  verbose
)

Arguments

Available Methods

- 'autoplot(object, type = "Fit")'

Examples

data("ParaSetEx")
data("NumOutEx")
ModelType <- "JPS original"
Economy <- "Brazil"
Fitgraphs(ModelType,
  WishFitgraphs = TRUE, ParaSetEx, NumOutEx, Economy, PathsGraphs = NULL,
  Folder2save = NULL, verbose = FALSE
)

Creates the folders and the path in which the graphical outputs are stored (Bootstrap version)

Description

Creates the folders and the path in which the graphical outputs are stored (Bootstrap version)

Usage

FolderCreationBoot(ModelType, Economies, Folder2save)

Arguments

Creates the folders and the path in which the graphical outputs are stored (point estimate version)

Description

Creates the folders and the path in which the graphical outputs are stored (point estimate version)

Usage

FolderCreationPoint(ModelType, Economies, Folder2save)

Arguments

Creates folder to store graphs generated from the bootstrap analysis

Description

Creates folder to store graphs generated from the bootstrap analysis

Usage

FolderCreation_Boot(
  ModelType,
  LabIRF,
  Economies,
  OutType,
  Folder2save,
  Ortho = FALSE
)

Arguments

Create folders for storing IRFs and GIRFs

Description

Create folders for storing IRFs and GIRFs

Usage

FolderPrep_FEVDs(
  OutputType,
  WishPdynamicsgraphs,
  WishYieldsgraphs,
  Economies,
  ModelType,
  Folder2Save
)

Arguments

Create folders for storing IRFs and GIRFs

Description

Create folders for storing IRFs and GIRFs

Usage

FolderPrep_IRFs(
  OutputType,
  WishPdynamicsgraphs,
  WishYieldsgraphs,
  Economies,
  ModelType,
  Folder2Save
)

Arguments

Generates forecasts of bond yields for all model types

Description

Generates forecasts of bond yields for all model types

Usage

ForecastYields(
  ModelType,
  ModelPara,
  InputsForOutputs,
  FactorLabels,
  Economies,
  JLLlist = NULL,
  GVARlist = NULL,
  WishBRW = FALSE,
  BRWlist = NULL,
  Folder2save = NULL,
  verbose = TRUE
)

Arguments

Value

An object of class 'ATSMModelForecast' containing the following elements:

1. Out-of-sample forecasts of bond yields per forecast horizon

2. Out-of-sample forecast errors of bond yields per forecast horizon

3. Root mean square errors per forecast horizon

Permissible options - forecast list (InputsForOutputs input)

• ForHoriz: forecast horizon. Must be a positive integer.

• t0Sample: initial sample date. Must be a positive integer smaller than the time series dimension of the model (Td)

• t0Forecast: last sample date for the first forecast. Note that Td > t0Forecast + ForHoriz.

• ForType: "Rolling" (rolling window forecast) or "Expanding" (for expanding window forecast)

Available Methods

- 'plot(object)'

Examples

data("ParaSetEx")
data("InpForOutEx")
# Adjust inputs according to the loaded features
ModelType <- "JPS original"
Economy <- "Brazil"
FacLab <- LabFac(N = 1, DomVar = "Eco_Act", GlobalVar = "Gl_Eco_Act", Economy, ModelType)
 # Adjust Forecasting setting
InpForOutEx[[ModelType]]$Forecasting <- list(
  WishForecast = 1, ForHoriz = 12, t0Sample = 1,
  t0Forecast = 143, ForType = "Expanding"
)

Forecast <- ForecastYields(ModelType, ParaSetEx, InpForOutEx, FacLab, Economy,
  WishBRW = FALSE, verbose = TRUE
)

Compute the forward premia for all models

Description

Compute the forward premia for all models

Usage

ForwardPremia(
  ModelPara,
  avexpFP,
  ModelType,
  FactorLabels,
  InputsForOutputs,
  Economies
)

Arguments

Use function ML to generate the outputs from a ATSM

Description

Use function ML to generate the outputs from a ATSM

Usage

FunctionML_vec(
  x,
  ML_fun,
  ListInputSet,
  ModelType,
  FactorLabels,
  Economies,
  JLLinputs,
  GVARinputs,
  WithEstimation
)

Arguments

Estimates a GVAR(1) and VARX(1,1,1) models

Description

Estimates a GVAR(1) and VARX(1,1,1) models

Usage

GVAR(GVARinputs, N, CheckInputs = FALSE)

Arguments

Value

list. Contains:

1. parameters of the country-specific VARX(1,1,1):

   • intercept (M + N x 1)

   • phi_1 (M + N x M + N)

   • phi_1* (M + N x M + N)

   • phi_g (M + N x M + N)

   • Sigma (M + N x G)

2. parameters of the GVAR:

   • F0 (K x K)

   • F1 (K x K)

   • Sigma_y (K x K)

General Notation

• C: number of countries in the system

• G: number of global unspanned factors

• M: number of country-specific unspanned factors

• N: number of country-specific spanned factors

• K: total number of risk factors (K = C x (N + M) + G)

References

Chudik, A. and Pesaran, M. H. (2016). "Theory and Practice of GVAR modelling" (Journal of Economic Surveys)

Examples

data(GVARFactors)

GVARinputs <- list(
  Economies = c("China", "Brazil", "Mexico", "Uruguay"),
  GVARFactors = GVARFactors, VARXtype = "unconstrained"
)

GVARinputs$Wgvar <- matrix(c(
  0, 0.83, 0.86, 0.38,
  0.65, 0, 0.13, 0.55,
  0.32, 0.12, 0, 0.07,
  0.03, 0.05, 0.01, 0
), nrow = 4, ncol = 4)
N <- 3

GVARPara <- GVAR(GVARinputs, N)

Data: Risk Factors for the GVAR - Candelon and Moura (2024, JFEC)

Description

Risk factors data used in the GVAR-ATSM from Candelon and Moura (2024, JFEC)

Usage

data("GVARFactors")

Format

List of risk factors organized for GVAR estimation. It includes global unspanned factors (economic activity, inflation) and domestic factors—both unspanned (economic activity, inflation) and spanned (level, slope, curvature) with their starred counterparts. The dataset covers Brazil, China, Mexico, and Uruguay at a monthly frequency from June 2004 to January 2020.

Source

Global unspanned factors

See data("GlobalMacro") for a detailed data description.

Domestic unspanned factors

See data("DomMacro") for a detailed data description.

Domestic spanned factors

First three principal components of each country set of bond yields. See data("Yields") for a detailed data description.

Domestic star factors

Weighted average of foreign factors. See Transition_Matrix for the computation of weights.

References

Candelon, B. and Moura, R. (2024) "A Multicountry Model of the Term Structures of Interest Rates with a GVAR". (Journal of Financial Econometrics)

Prepare risk factors for the estimation of the GVAR model

Description

Prepare risk factors for the estimation of the GVAR model

Usage

GVAR_PrepFactors(GVARinputs, DomLabels, StarLabels, GlobalLabels, N)

Arguments

Gather several forecast dates

Description

Gather several forecast dates

Usage

Gather_Forecasts(Forecast_OneDate, Forecast_AllDates, Economies, ModelType)

Arguments

computes the density function of a gaussian process

Description

computes the density function of a gaussian process

Usage

GaussianDensity(res, SSZ)

Arguments

Value

y vector of density (1 x T)

Generate artificial time-series in the bootstrap setup

Description

Generate artificial time-series in the bootstrap setup

Usage

Gen_Artificial_Series(
  ModelParaPE,
  residPdynOriginal,
  residYieOriginal,
  ModelType,
  BFull,
  InputsForOutputs,
  Economies,
  FactorLabels,
  GVARlist,
  JLLlist,
  WishBRW,
  BRWlist,
  verbose,
  nlag = 1
)

Arguments

Compute the bond yield forecast for any model type

Description

Compute the bond yield forecast for any model type

Usage

Gen_Forecast_Yields(
  K0Z,
  K1Z,
  A,
  Bfull,
  ZZsubsample,
  C,
  J,
  YieldsLabels,
  ForLabels,
  ForHoriz,
  ModelType
)

Arguments

Simulate N_Boot dataset from the P-dynamics

Description

Simulate N_Boot dataset from the P-dynamics

Usage

Gen_art_series(K1Z_j, N_Boot, RFs)

Arguments

Gathers the general inputs for model estimation

Description

Gathers the general inputs for model estimation

Usage

GeneralMLEInputs(
  Yields,
  RiskFactors,
  FactorLabels,
  mat,
  DataFrequency,
  Label_Multi_Models,
  Economies,
  ModelType,
  UnitYields
)

Arguments

Compute the auxiliary parameters a.

Description

Compute the auxiliary parameters a.

Usage

GetAuxPara(
  ParaValue,
  Const_Type_Full,
  Economies,
  FactorLabels,
  JLLinputs = NULL
)

Arguments

Generate the variable labels of the JLL models

Description

Generate the variable labels of the JLL models

Usage

GetLabels_JLL(NonOrthoFactors, JLLinputs, G)

Arguments

Generate the factor labels for models estimated on a country-by-country basis

Description

Generate the factor labels for models estimated on a country-by-country basis

Usage

GetLabels_sepQ(Economy, ModelType, FactorLabels)

Arguments

Compute the parameters used in the P-dynamics of the model

Description

Compute the parameters used in the P-dynamics of the model

Usage

GetPdynPara(
  RiskFactors,
  FactorLabels,
  Economies,
  ModelType,
  BRWinputs,
  GVARinputs,
  JLLinputs,
  CheckInputs = F,
  verbose
)

Arguments

Compute P-dynamics parameters using the bias correction method from BRW (2012)

Description

Compute P-dynamics parameters using the bias correction method from BRW (2012)

Usage

GetPdynPara_BC(
  ModelType,
  BRWinputs,
  RiskFactors,
  Economies,
  FactorLabels,
  GVARinputs,
  JLLinputs,
  verbose
)

Arguments

Compute P-dynamics parameters without using the bias correction method from BRW (2012)

Description

Compute P-dynamics parameters without using the bias correction method from BRW (2012)

Usage

GetPdynPara_NoBC(
  ModelType,
  RiskFactors,
  Economies,
  N,
  GVARinputs,
  JLLinputs,
  CheckInpts = F
)

Arguments

Map auxiliary (unconstrained) parameters a to constrained parameters b

Description

Map auxiliary (unconstrained) parameters a to constrained parameters b

Usage

GetTruePara(
  ParaValue,
  Const_Type_Full,
  FactorLabels,
  Economies,
  JLLinputs = NULL,
  GVARinputs = NULL
)

Arguments

Gather all country-specific yields in a single matrix of dimension CJ x T

Description

Gather all country-specific yields in a single matrix of dimension CJ x T

Usage

GetYields_AllCountries(ModelPara, Economies, ModelType)

Arguments

Compute the A loadings

Description

Compute the A loadings

Usage

Get_As(LoadBs, Wpca, r0, dt, Economies, ModelType)

Arguments

Compute the B matrix of loadings

Description

Compute the B matrix of loadings

Usage

Get_BFull(ModelParaPE, FactorLabels, mat, Economies, ModelType)

Arguments

Build the B loadings

Description

Build the B loadings

Usage

Get_Bs(mat, dt, K1XQ, SSZ, Wpca, FactorLabels, Economy, ModelType)

Arguments

Estimate feedback matrix from several models (No bias-corrected version)

Description

Estimate feedback matrix from several models (No bias-corrected version)

Usage

Get_FeedMat_NoBC(
  RiskFactors,
  ModelType,
  Economies,
  GVARinputs,
  JLLinputs,
  FactorLabels,
  CheckInpts = FALSE
)

Arguments

Get the intercept, feedback matrix and the variance-covariance matrix from GVAR without global factors

Description

Get the intercept, feedback matrix and the variance-covariance matrix from GVAR without global factors

Usage

Get_G0G1Sigma(ParaVARX, GVARinputs, Ai0, Ai1, Wi)

Arguments

Compute the feedback matrix from a GVAR model with global factors

Description

Compute the feedback matrix from a GVAR model with global factors

Usage

Get_Gy1(ParaVARX, GVARinputs, G1, Phi_w1)

Arguments

Compute the variance-covariance matrix after the bias correction procedure

Description

Compute the variance-covariance matrix after the bias correction procedure

Usage

Get_SSZ_BC(K1Z_BC, RiskFactors, GVARinputs, JLLinputs, FactorLabels, ModelType)

Arguments

Compute the variance-covariance matrix of the bond yields

Description

Compute the variance-covariance matrix of the bond yields

Usage

Get_SigmaYields(YieldsTS, N, mat, WpcaFull, se, ModelType)

Arguments

Compute Sigmas/Cholesky factorizations

Description

Compute Sigmas/Cholesky factorizations

Usage

Get_Sigma_JLL(JLLinputs, FacSet, Para_Ortho_Reg, Para_Ortho_VAR, N)

Arguments

Collect both the domestic and global unspanned factors of all countries in single matrices

Description

Collect both the domestic and global unspanned factors of all countries in single matrices

Usage

Get_Unspanned(ModelPara, FactorLabels, Economies, ModelType)

Arguments

Compute the cross-section loadings of yields of a canonical A0_N model

Description

Compute the cross-section loadings of yields of a canonical A0_N model

Usage

Get__BnXAnX(mat, K1XQ, ModelType, r0 = NULL, SSX = NULL, Economies)

Arguments

References

• Dai, Q. and Singleton, K. (2000). "Specification Analysis of Affine Term Structure Models". The Journal of Finance.

• Joslin, S., Singleton, K. and Zhu, H. (2011). "A new perspective on Gaussian dynamic term structure models". The Review of Financial Studies.

Obtain the country-specific a0

Description

Obtain the country-specific a0

Usage

Get_a0(GVARinputs, ParaVARX)

Arguments

Compute the log-likelihood function

Description

Compute the log-likelihood function

Usage

Get_llk(P, Y, Z, N, mat, We, Wpca, K0Z, K1Z, SSZ, LoadBs, LoadAs, ModelType)

Arguments

Compute long-run risk neutral mean (r0) for the various models

Description

Compute long-run risk neutral mean (r0) for the various models

Usage

Get_r0(Y, P, N, mat, dt, B_list, Wpca, We, Economies, ModelType)

Arguments

Get delta t

Description

Get delta t

Usage

Getdt(DataFrequency)

Arguments

Data: Risk Factors - Candelon and Moura (2024, JFEC)

Description

Global risk factors data used in Candelon and Moura (2024, JFEC)

Usage

data("GlobalMacro")

Format

A matrix containing the time series of global risk factors, namely global economic activity and global inflation. The data have monthly frequency and span the period from June/2004 to January/2020.

Source

Global economic activity

Lutz Kilian’s index of global real economic activity <https://sites.google.com/site/lkilian2019/research/data-sets?authuser=0>

Global inflation

year-over-year variation of the OECD aggregated CPI containing all its state members <https://www.oecd.org/en/data/indicators/inflation-cpi.html>

References

Candelon, B. and Moura, R. (2024) "A Multicountry Model of the Term Structures of Interest Rates with a GVAR". (Journal of Financial Econometrics)

Data: Risk Factors - Candelon and Moura (2023, EM)

Description

Global risk factors data used in Candelon and Moura (2023)

Usage

data("GlobalMacro_covid")

Format

A matrix containing the time series of global risk factors, namely the year-over-year growth rates of U.S. and Chinese output, and the S&P 500 index. The data have weekly frequency and span the period from March 22, 2020, to September 26, 2021.

Source

U.S. output growth:

OECD Weekly Tracker index <https://web-archive.oecd.org/sections/weekly-tracker-of-gdp-growth/index.htm>

China output growth:

weekly year-over-year change in the interpolated OECD leading indicator <https://www.oecd.org/en/data/indicators/composite-leading-indicator-cli.html>

S&P-500:

year-over-year variation from the Standard and Poor’s 500 stock market index. Simulated data constructed using FRED series.

References

Candelon, B. and Moura, R. (2023) "Sovereign yield curves and the COVID-19 in emerging markets". (Economic Modelling)

Generate the graphical outputs for the selected models (Point estimate)

Description

Generate the graphical outputs for the selected models (Point estimate)

Usage

GraphicalOutputs(
  ModelType,
  ModelPara,
  NumOut,
  InputsForOutputs,
  Economies,
  FactorLabels,
  Folder2save,
  verbose
)

Arguments

Find the indexes of zero-restrictions from the orthogonalized variance-covariance matrix from the JLL-based models

Description

Find the indexes of zero-restrictions from the orthogonalized variance-covariance matrix from the JLL-based models

Usage

IDXZeroRestrictionsJLLVarCovOrtho(M, N, G, Economies, DomUnit)

Arguments

Value

restricted version of the JLL of the Cholesky factorization (F x F)

IRFs and GIRFs for all models

Description

IRFs and GIRFs for all models

Usage

IRFandGIRF(ModelType, ModelPara, IRFhoriz, FactorLabels, Economies)

Arguments

Details

The Structural shocks from the IRFs are identified via Cholesky decomposition

IRFs and GIRFs after bootstrap for all models

Description

IRFs and GIRFs after bootstrap for all models

Usage

IRFandGIRF_BS(ModelType, ModelParaBoot, IRFhoriz, FactorLabels, Economies)

Arguments

Creates the confidence bounds and the graphs of IRFs and GIRFs after bootstrap

Description

Creates the confidence bounds and the graphs of IRFs and GIRFs after bootstrap

Usage

IRFandGIRFbs(
  ModelType,
  ModelBootstrap,
  NumOutPE,
  InputsForOutputs,
  Economies,
  PathsGraphs,
  Folder2save,
  verbose
)

Arguments

IRF and GIRF graphs for all models

Description

IRF and GIRF graphs for all models

Usage

IRFandGIRFgraphs(
  ModelType,
  NumOut,
  WishPdynamicsgraphs,
  WishYieldsgraphs,
  IRFhoriz,
  PathsGraphs,
  OutputType,
  Economies,
  Folder2save,
  verbose
)

Arguments

Available Methods

- 'autoplot(object, type = "IRF_Factor")', 'autoplot(object, type = "IRF_Yields")', 'autoplot(object, type = "GIRF_Yields")', 'autoplot(object, type = "GIRF_Yields")'. For JLL-based models: 'autoplot(object, type = "IRF_Factor-_Ortho")',
'autoplot(object, type = "IRF_Yields_Ortho")', 'autoplot(object, type = "GIRF_Yields_Ortho")', 'autoplot(object, type = "GIRF_Yields_Ortho")'.

Examples

data("NumOutEx")
ModelType <- "JPS original"
Economy <- "Brazil"
IRFhoriz <- 20
irf_Out <- IRFandGIRFgraphs(ModelType, NumOutEx,
  WishPdynamicsgraphs = FALSE, WishYieldsgraphs = TRUE, IRFhoriz,
  PathsGraphs = NULL, OutputType = "GIRF", Economy, Folder2save = NULL,
  verbose = FALSE
)

Gather data for IRFs and GIRFs grahs (version "Factors")

Description

Gather data for IRFs and GIRFs grahs (version "Factors")

Usage

IRFandGIRFs_Format_Fac(IRFFac)

Arguments

Gather data for IRFs and GIRFs grahs (version "Yields")

Description

Gather data for IRFs and GIRFs grahs (version "Yields")

Usage

IRFandGIRFs_Format_Yields(IRFYields)

Arguments

Find the indexes of the spanned factors

Description

Find the indexes of the spanned factors

Usage

IdxAllSpanned(ModelType, FactorLabels, Economies)

Arguments

Extract the indexes related to the spanned factors in the variance-covariance matrix

Description

Extract the indexes related to the spanned factors in the variance-covariance matrix

Usage

IdxSpanned(G, M, N, C)

Arguments

Obtain the indexes of both the domestic and global unspanned factors

Description

Obtain the indexes of both the domestic and global unspanned factors

Usage

Idx_UnspanFact(RiskFactors_TS, FactorLabels, Economies)

Arguments

Impose stationary constraint under the risk-neutral measure

Description

Impose stationary constraint under the risk-neutral measure

Usage

ImposeStat_Aux(yy, ub = 0.9999, lb = 1e-04)

Arguments

Makes sure that the stationary constraint under the risk-neutral measure is preserved

Description

Makes sure that the stationary constraint under the risk-neutral measure is preserved

Usage

ImposeStat_True(params, K1Q, ub = 0.9999, lb = 1e-04)

Arguments

Example of list inputs used in the construction of several model outputs

Description

List of inputs of a JPS-based model for Brazilian data

Usage

data("InpForOutEx")

Format

list of inputs

Generates inputs necessary to build the likelihood function for the ATSM model

Description

Generates inputs necessary to build the likelihood function for the ATSM model

Usage

InputsForOpt(
  InitialSampleDate,
  FinalSampleDate,
  ModelType,
  Yields,
  GlobalMacro,
  DomMacro,
  FactorLabels,
  Economies,
  DataFrequency,
  GVARlist = NULL,
  JLLlist = NULL,
  WishBRW = FALSE,
  BRWlist = NULL,
  UnitYields = "Month",
  CheckInputs = TRUE,
  BS_Adj = FALSE,
  verbose = TRUE
)

Arguments

Value

An object of class 'ATSMModelInputs' containing the necessary inputs for performing the model optimization.

Permissible options for GVARlist

• VARXtype: "unconstrained" or "constrained"

• W_type: "Time-varying" or "Sample Mean"

• t_First_Wgvar, t_Last_Wgvar: year as character

Permissible options for JLLlist

• DomUnit: name of the dominant economy or None

• WishSigmas: TRUE (estimate variance-covariance matrices) or FALSE

• SigmaNonOrtho: NULL or K x K matrix

Permissible options for BRWlist

• BiasCorrection: TRUE (bias-corrected) or FALSE

• flag_mean: TRUE (mean) or FALSE (median)

• gamma: numeric adjustment parameter

• N_iter: number of iterations

• N_burn: number of burn-in iterations

• B: number of bootstrap samples

• checkBRW: TRUE or FALSE

• B_check: number of bootstrap samples for closeness check

General Notation

• Td model time series dimension.

• C number of countries in the system.

• G number of global unspanned factors.

• M number of country-specific unspanned factors.

• K total number of risk factors.

• J number of bond yields per country used in estimation.

Available Methods

- 'print(object)' - 'summary(object)'

Examples

# Example 1:
data(GlobalMacro)
data(DomMacro)
data(Yields)

ModelType <- "JPS original"
Economies <- "Mexico"
t0 <- "01-05-2007" # Initial Sample Date (Format: "dd-mm-yyyy")
tF <- "01-12-2018" # Final Sample Date (Format: "dd-mm-yyyy")
N <- 3
GlobalVar <- c("Gl_Eco_Act") # Global Variables
DomVar <- c("Eco_Act") # Domestic Variables
FactorLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)

DataFreq <- "Monthly"

ATSMInputs <- InputsForOpt(t0, tF, ModelType, Yields, GlobalMacro, DomMacro,
  FactorLabels, Economies, DataFreq,
  CheckInputs = FALSE, verbose = FALSE
)

# Example 2:
LoadData("CM_2024")

ModelType <- "GVAR multi"

Economies <- c("China", "Brazil", "Mexico", "Uruguay")
t0 <- "01-05-2007" # InitialSampleDate (Format: "dd-mm-yyyy")
tF <- "01-12-2019" # FinalSampleDate (Format: "dd-mm-yyyy")
N <- 2
GlobalVar <- c("Gl_Eco_Act", "Gl_Inflation") # Global Variables
DomVar <- c("Inflation") # Domestic Variables
FactorLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)

DataFreq <- "Monthly"
GVARlist <- list(
  VARXtype = "unconstrained", W_type = "Sample Mean",
  t_First_Wgvar = "2007", t_Last_Wgvar = "2019", DataConnectedness = TradeFlows
)

ATSMInputs <- InputsForOpt(t0, tF, ModelType, Yields, GlobalMacro, DomMacro,
  FactorLabels, Economies, DataFreq, GVARlist,
  CheckInputs = FALSE, verbose = FALSE
)

# Example 3:
LoadData("CM_2024")

ModelType <- "JLL original"

Economies <- c("China", "Brazil", "Uruguay")
t0 <- "01-05-2007" # InitialSampleDate (Format: "dd-mm-yyyy")
tF <- "01-12-2019" # FinalSampleDate (Format: "dd-mm-yyyy")
N <- 2
GlobalVar <- c("Gl_Eco_Act", "Gl_Inflation") # Global Variables
DomVar <- c("Eco_Act", "Inflation") # Domestic Variables
FactorLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)

JLLinputs <- list(DomUnit = "China")

DataFrequency <- "Monthly"

ATSMInputs <- InputsForOpt(t0, tF, ModelType, Yields, GlobalMacro, DomMacro,
  FactorLabels, Economies, DataFreq,
  JLLlist = JLLinputs,
  CheckInputs = FALSE, verbose = FALSE
)

Collects the inputs that are used to construct the numerical and graphical outputs

Description

Collects the inputs that are used to construct the numerical and graphical outputs

Usage

InputsForOutputs(
  ModelType,
  Horiz,
  ListOutputWished,
  OutputLabel,
  WishStationarityQ,
  DataFrequency,
  WishGraphYields = FALSE,
  WishGraphRiskFactors = FALSE,
  WishOrthoJLLgraphs = FALSE,
  WishForwardPremia = FALSE,
  LimFP = NULL,
  WishBootstrap = FALSE,
  ListBoot = NULL,
  WishForecast = FALSE,
  ListForecast = NULL,
  UnitYields = "Month"
)

Arguments

Value

List of necessary inputs to generate the graphs and outputs of the desired model.

Examples

ModelType <- "JPS original"
Horiz <- 100
DesiredOutputGraphs <- c("Fit", "GIRF", "GFEVD")
OutputLabel <- "Test"
WishStationarityQ <- TRUE
WishGraphRiskFac <- FALSE
WishGraphYields <- TRUE

InputsList <- InputsForOutputs(
  ModelType, Horiz, DesiredOutputGraphs, OutputLabel,
  WishStationarityQ, WishGraphYields, WishGraphRiskFac
)

Fit the cross-section of yields using spline

Description

Fit the cross-section of yields using spline

Usage

Intra_Yields(Yields, mat_vec, time_step)

Arguments

Robust method for matrix inversion

Description

Robust method for matrix inversion

Usage

InvMat_Robust(M)

Arguments

Estimates the P-dynamics from JLL-based models

Description

Estimates the P-dynamics from JLL-based models

Usage

JLL(NonOrthoFactors, N, JLLinputs, CheckInputs = FALSE)

Arguments

Value

List of model parameters from both the orthogonalized and non-orthogonalized versions of the JLL-based models

General Notation

• Td: model time series dimension

• C number of countries in the system.

• K: total number of risk factors

References

Jotiskhatira, P. ; Le, A. and Lundblad, C. (2015). "Why do interest rates in different currencies co-move?" (Journal of Financial Economics)

Examples

data(RiskFacFull)
RF_TS <- RiskFacFull
N <- 3
JLLinputs <- list(
  Economies = c("China", "Brazil", "Mexico", "Uruguay"), DomUnit = "China",
  WishSigmas = TRUE, SigmaNonOrtho = NULL, JLLModelType = "JLL original"
)
JLLPara <- JLL(RF_TS, N, JLLinputs)

Main Jacobian approximation

Description

Main Jacobian approximation

Usage

Jac_approx(f, x, nlevels = 5L)

Arguments

References

Le, A., & Singleton, K. J. (2018). Small Package of Matlab Routines for Estimation of Some Term Structure Models. EABCN Training School.
This function offers an independent R implementation that is informed by the conceptual framework outlined in Le and Singleton (2018), but adapted to the present modeling context.

Convert a Matrix to Jordan-Like Form for Term Structure Models

Description

Convert a Matrix to Jordan-Like Form for Term Structure Models

Usage

JordanMat(matrix_in)

Arguments

Value

A matrix in a specialized block form used in term structure modeling

References

• The mathematical approach is based on methods described in: Dai, Q., & Singleton, K. J. (2000). Specification Analysis of Affine Term Structure Models. The Journal of Finance, 55(5), 1943-1978.

• Le, A., & Singleton, K. J. (2018). Small Package of Matlab Routines for Estimation of Some Term Structure Models. EABCN Training School.

• For theoretical background on Jordan forms in term structure models: Duffee, G. R. (2002). Term Premia and Interest Rate Forecasts in Affine Models. The Journal of Finance, 57(1), 405-443.

Check for JLL models for Jordan restrictions (auxiliary form)

Description

Check for JLL models for Jordan restrictions (auxiliary form)

Usage

Jordan_JLL(ParaValue, C, N)

Arguments

Impose stationarity under the Q-measure

Description

Impose stationarity under the Q-measure

Usage

K1XQStationary(StationaryEigenvalues)

Arguments

Generates the labels for risk factors used in the model

Description

Generates the labels for risk factors used in the model

Usage

LabFac(N, DomVar, GlobalVar, Economies, ModelType)

Arguments

Value

List containing the risk factor labels for spanned, domestic, star, and global variables, as well as tables for each country and all countries.

Examples

N <- 2
DomVar <- c("inflation", "Output gap")
GlobalVar <- "Commodity Prices"
Economies <- c("U.S.", "Canada", "Germany", "Japan")
ModelType <- "JPS original"
VarLabels <- LabFac(N, DomVar, GlobalVar, Economies, ModelType)

Generate the labels of the spanned factors

Description

Generate the labels of the spanned factors

Usage

LabelsSpanned(N)

Arguments

Generate the labels of the star variables

Description

Generate the labels of the star variables

Usage

LabelsStar(FactorLabels)

Arguments

Loads data sets from several papers

Description

Loads data sets from several papers

Usage

LoadData(DataPaper)

Arguments

Value

Complete set of data from several papers.

References

1. Bauer and Rudebusch (2017). "Resolving the Spanning Puzzle in Macro-Finance Term Structure Models" (Review of Finance)

2. Candelon and Moura (2023). "Sovereign yield curves and the COVID-19 in emerging markets" (Economic Modelling)

3. Candelon and Moura (2024). "A Multicountry Model of the Term Structures of Interest Rates with a GVAR" (Journal of Financial Econometrics)

Examples

# Example 1:
LoadData("BR_2017")

# Example 2:
LoadData("CM_2023")

# Example 3:
LoadData("CM_2024")

Read data from Excel files and return a named list of data frames

Description

Read data from Excel files and return a named list of data frames

Usage

Load_Excel_Data(ExcelFilePath)

Arguments

Details

Uses the readxl package to read all sheets from the specified Excel file. Each sheet is returned as a data frame. The output is a named list, with names matching the sheet names in the Excel file.

Value

Named list of data frames, one for each sheet in the Excel file. The names of the list elements correspond to the sheet names.

Examples

if (!requireNamespace("readxl", quietly = TRUE)) {
  stop(
    "Please install package \"readxl\" to use this feature.",
    call. = FALSE
  )

  Load_Excel_Data(system.file("extdata", "MacroData.xlsx", package = "MultiATSM"))
  Load_Excel_Data(system.file("extdata", "YieldsData.xlsx", package = "MultiATSM"))
}

Compute the maximum likelihood function of all models

Description

Compute the maximum likelihood function of all models

Usage

MLEdensity(
  K1XQ,
  r0,
  SSZ,
  K0Z,
  K1Z,
  se,
  Gy.0,
  mat,
  Y,
  Z,
  P,
  Wpca,
  We,
  WpcaFull,
  dt,
  Economies,
  FactorLabels,
  ModelType,
  GVARinputs = NULL,
  JLLinputs = NULL,
  BS_outputs = FALSE,
  ExportListOut = TRUE
)

Arguments

References

• Candelon, C. and Moura, R. (2024). “A Multicountry Model of the Term Structures of Interest Rates with a GVAR.” Journal of Financial Econometrics 22 (5): 1558–87.

• Jotikasthira, C; Le, A. and Lundblad, C (2015). “Why Do Term Structures in Different Currencies Co-Move?” Journal of Financial Economics 115: 58–83.

• Joslin, S,; Priebsch, M. and Singleton, K. (2014). “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks.” Journal of Finance 69 (3): 1197–1233.

• Joslin, S., Singleton, K. and Zhu, H. (2011). "A new perspective on Gaussian dynamic term structure models". The Review of Financial Studies.

• Le, A. and Singleton, K. (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.

Set up the vector-valued objective function (Point estimate)

Description

Set up the vector-valued objective function (Point estimate)

Usage

MLFunction(
  MLEinputs,
  Economies,
  DataFrequency,
  FactorLabels,
  ModelType,
  BS_outType = FALSE
)

Arguments

Value

objective function

Prevents algorithm to end up in ill-defined likelihood

Description

Prevents algorithm to end up in ill-defined likelihood

Usage

ML_stable(par, MLvec)

Arguments

Mean of the llk function used in the estimation of the selected ATSM

Description

Mean of the llk function used in the estimation of the selected ATSM

Usage

MLtemporary(xtemp, scaling_vector, MLvec)

Arguments

Estimate the marginal model for the global factors

Description

Estimate the marginal model for the global factors

Usage

MarginalModelPara(GVARinputs)

Arguments

Adjust vector of maturities

Description

Adjust vector of maturities

Usage

MatAdjusted(mat, UnitYields)

Arguments

Create a vector of numerical maturities in years

Description

Create a vector of numerical maturities in years

Usage

Maturities(DataYields, Economies, UnitYields)

Arguments

Value

Vector containing all observed maturities expressed in years

Limit the number of categories in FEVDs and GFEVDs graphs by merging small groups into other

Description

Limit the number of categories in FEVDs and GFEVDs graphs by merging small groups into other

Usage

MergeFEVD_graphs(FEVDlist, Threshold = 0.05)

Arguments

Overview of Datasets Included in the MultiATSM Package

Description

The package includes several pre-processed datasets used for estimation and replication examples:

Details

GlobalMacro

Global macro-financial risk factors, namely global economic activity and global inflation.

GlobalMacro_covid

Global macro-financial risk factors, namely the output growth rate from the U.S. and China and the S&P 500 index.

DomMacro

Domestic macroeconomic risk factors, namely economic activity and inflation.

DomMacro_covid

Domestic macroeconomic risk factors, namely otput growth, inflation, CDS and the COVID-19 reproduction rate

TradeFlows

Bilateral trade flow series used in GVAR examples as a proxy measure of cross-country conectdness.

TradeFlows_covid

Bilateral trade flow series used in GVAR examples as a proxy measure of cross-country conectdness.

Yields

Monthly series of bond yields by maturity for multiple economies.

Yields_covid

Weekly series of sovereign bond yields by maturity for multiple economies.

RiskFacFull

Full set of risk factors (global and domestic) data used throughout the package

GVARFactors

List of risk factors used in the estimation of GVAR models.

BR_jps_out

Replications of the JPS outputs by Bauer and Rudebusch (2017)

InpForOutEx

List of inputs for an illustrative JPS model with Brazilian data

ParaSetEx

List of set of parameterafter optimization for an illustrative JPS model with Brazilian data

NumOutEx

List of numerical outputs for an illustrative JPS model with Brazilian data

Out_Example

re-loaded examaple of a complete list of several model outputs. Used in the package vignette.

Each dataset is documented separately using '?GlobalMacro', '?DomMacro', '?TradeFlows', '?Yields', etc. Datasets ending with the suffix _covid are based on those used in Candelon and Moura (2023) and cover Brazil, India, Mexico, and Russia. The remaining datasets correspond to Candelon and Moura (2024) and include Brazil, China, Mexico, and Uruguay.

References

1. Candelon, B. and Moura, R. (2023) "Sovereign yield curves and the COVID-19 in emerging markets". (Economic Modelling)

2. Candelon, B. and Moura, R. (2024) "A Multicountry Model of the Term Structures of Interest Rates with a GVAR". (Journal of Financial Econometrics)

Obtain the non-orthogonalized model parameters

Description

Obtain the non-orthogonalized model parameters

Usage

NoOrthoVAR_JLL(Para_Ortho_Reg, Para_Ortho_VAR)

Arguments

Example of computed numerical outputs

Description

Numerical outputs for JPS-based model using Brazilian data

Usage

data("NumOutEx")

Format

list of inputs and outputs

PC var explained

variance explained per spanned factor

Fit

model fit of bond yields

IRF

Impulse response function

FEVD

Forecast error variance decomposition

GIRF

Generalized impulse response function

GFEVD

Generalized Forecast error variance decomposition

TermPremiaDecomp

Term Premia decomposition

Constructs the model numerical outputs (model fit, IRFs, GIRFs, FEVDs, GFEVDs, and term premia)

Description

Constructs the model numerical outputs (model fit, IRFs, GIRFs, FEVDs, GFEVDs, and term premia)

Usage

NumOutputs(
  ModelType,
  ModelPara,
  InputsForOutputs,
  FactorLabels,
  Economies,
  Folder2save = NULL,
  verbose = TRUE
)

Arguments

Details

Both IRFs and FEVDs are computed using the Cholesky decomposition method. The risk factors are ordered as follows: (i) global unspanned factors, and (ii) domestic unspanned and spanned factors for each country. The order of countries follows the sequence defined in the Economies vector.

Value

An object of class 'ATSMNumOutputs' containing the following keys elements:

1. Model parameter estimates

2. Model fit of bond yields

3. IRFs

4. FEVDs

5. GIRFs

6. GFEVDs

7. Bond yield decomposition

Available methods

- 'autoplot(object, type)'

References

Pesaran, H. Hashem, and Shin, Yongcheol. "Generalized impulse response analysis in linear multivariate models." Economics letters 58.1 (1998): 17-29.

Examples

data("ParaSetEx")
data("InpForOutEx")
# Adjust inputs according to the loaded features
ModelType <- "JPS original"
Economy <- "Brazil"
FacLab <- LabFac(N = 1, DomVar = "Eco_Act", GlobalVar = "Gl_Eco_Act", Economy, ModelType)

NumOut <- NumOutputs(ModelType, ParaSetEx, InpForOutEx, FacLab, Economy,
  Folder2save = NULL, verbose = FALSE
)

Numerical outputs (IRFs, GIRFs, FEVD, and GFEVD) for bootstrap

Description

Numerical outputs (IRFs, GIRFs, FEVD, and GFEVD) for bootstrap

Usage

NumOutputs_Bootstrap(
  ModelType,
  ModelParaBoot,
  InputsForOutputs,
  FactorLabels,
  Economies
)

Arguments

Perform out-of-sample forecast of bond yields

Description

Perform out-of-sample forecast of bond yields

Usage

OOS_Forecast(
  ForHoriz,
  t_Last,
  ModelParaList,
  FactorLabels,
  Yields_FullSample,
  Economies,
  ModelType
)

Arguments

Prepare outputs to export after the model optimization

Description

Prepare outputs to export after the model optimization

Usage

OptOutputs(
  Y,
  Z,
  mat,
  N,
  dt,
  Wpca,
  K1XQ,
  SSZ,
  LoadAs,
  LoadBs,
  r0,
  se,
  K0Z,
  K1Z,
  Gy.0,
  VarYields,
  y,
  GVARinputs,
  JLLinputs,
  Economies,
  ModelType,
  BS_out = FALSE
)

Arguments

Perform the optimization of the log-likelihood function of the chosen ATSM

Description

Perform the optimization of the log-likelihood function of the chosen ATSM

Usage

Optimization(
  MLEinputs,
  StatQ,
  DataFreq,
  FactorLabels,
  Economies,
  ModelType,
  tol = 1e-04,
  EstType = c("BFGS", "Nelder-Mead"),
  TimeCount = TRUE,
  BS_outputs = FALSE,
  verbose = TRUE
)

Arguments

Value

An object of class 'ATSMModelOutputs' containing model outputs after the optimization of the chosen ATSM specification.

Available Methods

- 'summary(object)'

References

• Candelon, C. and Moura, R. (2024). “A Multicountry Model of the Term Structures of Interest Rates with a GVAR.” Journal of Financial Econometrics 22 (5): 1558–87.

• Jotikasthira, C; Le, A. and Lundblad, C (2015). “Why Do Term Structures in Different Currencies Co-Move?” Journal of Financial Economics 115: 58–83.

• Joslin, S,; Priebsch, M. and Singleton, K. (2014). “Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks.” Journal of Finance 69 (3): 1197–1233.

• Joslin, S., Singleton, K. and Zhu, H. (2011). "A new perspective on Gaussian dynamic term structure models". The Review of Financial Studies.

• Le, A. and Singleton, K. (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.

Examples

LoadData("CM_2024")
ModelType <- "JPS original"
Economy <- "Brazil"
t0 <- "01-05-2007" # Initial Sample Date (Format: "dd-mm-yyyy")
tF <- "01-12-2018" # Final Sample Date (Format: "dd-mm-yyyy")
N <- 1
GlobalVar <- "Gl_Eco_Act" # Global Variables
DomVar <- "Eco_Act" # Domestic Variables
DataFreq <- "Monthly"
StatQ <- FALSE

FacLab <- LabFac(N, DomVar, GlobalVar, Economy, ModelType)
ATSMInputs <- InputsForOpt(t0, tF, ModelType, Yields, GlobalMacro, DomMacro,
  FacLab, Economy, DataFreq,
  CheckInputs = FALSE, verbose = FALSE
)

OptPara <- Optimization(ATSMInputs, StatQ, DataFreq, FacLab, Economy, ModelType, verbose = FALSE)

Optimization routine for the entire selected ATSM

Description

Optimization routine for the entire selected ATSM

Usage

OptimizationSetup_ATSM(x0, MLvec, EstType, tol = 1e-04, verbose = FALSE)

Arguments

Perform the minimization of ML function

Description

Perform the minimization of ML function

Usage

Optimization_PE(
  ML_fun,
  ListInputSet,
  FactorLabels,
  Economies,
  ModelType,
  JLLinputs = NULL,
  GVARinputs = NULL,
  tol = 1e-04,
  EstType,
  TimeCount = TRUE,
  verbose
)

Arguments

Compute the time elapsed in the numerical optimization

Description

Compute the time elapsed in the numerical optimization

Usage

Optimization_Time(start_time, verbose)

Arguments

Get coefficients from the orthogonalized regressions

Description

Get coefficients from the orthogonalized regressions

Usage

OrthoReg_JLL(JLLinputs, N, FacSet, FactorLab_NonOrth, FactorLab_JLL)

Arguments

VAR(1) with orthogonalized factors (JLL models)

Description

VAR(1) with orthogonalized factors (JLL models)

Usage

OrthoVAR_JLL(NonOrthoFactors, JLLinputs, Ortho_Set, FactLabels, N)

Arguments

Complete list of several outputs from an ATSM

Description

Example for illustration used in the package vignette

Usage

data("Out_Example")

Format

several model classes

ModelParaList

List of parameter estimates of the selected ATSM

ATSMinputs

General inputs from an ATSM

Forecasts

List of forecast outputs

NumOut

List of numerical outputs

Bootstrap

List of set of outputs after bootstrap

Numerical outputs (variance explained, model fit, IRFs, GIRFs, FEVDs, GFEVDs, and risk premia decomposition) for all models

Description

Numerical outputs (variance explained, model fit, IRFs, GIRFs, FEVDs, GFEVDs, and risk premia decomposition) for all models

Usage

OutputConstruction(
  ModelType,
  ModelPara,
  InputsForOutputs,
  FactorLabels,
  Economies,
  verbose = TRUE
)

Arguments

Prepares inputs to export

Description

Prepares inputs to export

Usage

Outputs2exportMLE(
  Label_Multi_Models,
  Economies,
  RiskFactors,
  Yields,
  mat,
  ModelInputsGen,
  ModelInputsSpec,
  PdynPara,
  ModelType
)

Arguments

Create the variable labels used in the estimation

Description

Create the variable labels used in the estimation

Usage

ParaLabelsOpt(ModelType, WishStationarityQ, MLEinputs, BS_outputs = FALSE)

Arguments

Example of parameter set after optimization

Description

JPS-based model for Brazilian data

Usage

data("ParaSetEx")

Format

list of inputs and outputs

Inupts

general model inputs

ModEst

model parameters estimates (JPS form)

Compute some key parameters from the P-dynamics (Bootstrap set)

Description

Compute some key parameters from the P-dynamics (Bootstrap set)

Usage

PdynResid_BS(ModelType, Economies, ModelPara_PE)

Arguments

Compute the root mean square error for all models

Description

Compute the root mean square error for all models

Usage

RMSE(ForecastOutputs)

Arguments

Perform a linear regression using demeaned variables

Description

Perform a linear regression using demeaned variables

Usage

Reg_demean(LHS, RHS)

Arguments

Value

Beta coefficients

Exclude series that contain NAs

Description

Exclude series that contain NAs

Usage

RemoveNA(YieldsData, MacroData, Economies)

Arguments

Value

return the time series data that were not initially composed by NAs.

Compute the residuals from the original model

Description

Compute the residuals from the original model

Usage

ResampleResiduals_BS(
  residPdynOriginal,
  residYieOriginal,
  InputsForOutputs,
  ModelType,
  nlag = 1
)

Arguments

Data: Full set of risk factors - Candelon and Moura (2024, JFEC)

Description

Full set of risk factors data used in Candelon and Moura (2024, JFEC)

Usage

data("RiskFacFull")

Format

matrix containing the full risk factors: (i) global unspanned factors (global economic activity and global inflation); (ii) domestic unspanned factors (economic activity and inflation); and (iii) domestic spanned factors (level, slope, and curvature). Economic system is formed by Brazil, China, Mexico and Uruguay. The data have monthly frequency and span the period from June/2004 to January/2020.

Source

Global unspanned factor

See data("GlobalMacro") for a detailed data description.

Domestic unspanned factor

See data("DomMacro") for a detailed data description.

Domestic spanned factor

First three principal components of each country set of bond yields. See data("Yields") for a detailed data description.

References

Candelon, B. and Moura, R. (2024) "A Multicountry Model of the Term Structures of Interest Rates with a GVAR". (Journal of Financial Econometrics)

Spanned and unspanned factors plot

Description

Spanned and unspanned factors plot

Usage

RiskFactorsGraphs(
  ModelType,
  WishRFgraphs,
  ModelOutputs,
  Economies,
  FactorLabels,
  Folder2save,
  verbose
)

Arguments

Available Methods

- 'autoplot(object, type = "RiskFactors")'

Examples

data("ParaSetEx")
# Adapt factor labels according to the example
ModelType <- "JPS original"
Economy <- "Brazil"
FacLab <- LabFac(N = 1, DomVar = "Eco_Act", GlobalVar = "Gl_Eco_Act", Economy, ModelType)

RiskFactorsGraphs(ModelType,
  WishRFgraphs = FALSE, ParaSetEx, Economy, FacLab,
  Folder2save = NULL, verbose = FALSE
)

Builds the complete set of time series of the risk factors (spanned and unspanned)

Description

Builds the complete set of time series of the risk factors (spanned and unspanned)

Usage

RiskFactorsPrep(
  FactorSet,
  Economies,
  FactorLabels,
  Initial_Date,
  Final_Date,
  DataFrequency
)

Arguments

Value

Risk factors used in the estimation of the desired ATSM

Compute the root of the eigenvalue of K1h

Description

Compute the root of the eigenvalue of K1h

Usage

RootEigen(K1_h, horiz, N)

Arguments

Rotate latent states to observed ones

Description

Rotate latent states to observed ones

Usage

Rotate_Lat_Obs(X_List, U1, U0)

Arguments

Stochastic approximation algorithm

Description

Stochastic approximation algorithm

Usage

SA_algorithm(
  K1Z_NoBC,
  RiskFactors,
  BRWlist,
  GVARinputs,
  JLLinputs,
  FactorLabels,
  Economies,
  ModelType,
  verbose
)

Arguments