Package 'VARshrink'

Coefficient matrices of endogenous variables

Description

Returns the estimated coefficient matrices of the lagged endogenous variables of a VAR(p) model. This is a modification of vars::Acoef() for the class "varshrinkest".

Usage

Acoef_sh(x)

Arguments

x	An object of class "varshrinkeset", generated by VARshrink().

Details

Consider VAR(p) model:

$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + C d_t + e_t .$

The function returns the K-by-K matrices A_1, ..., A_p as a list object.

Value

A list object with K-by-K VAR coefficient matrices A_1, A_2, ..., A_p

See Also

Acoef

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
Acoef_sh(estim)

---

ARCH-LM test

Description

Performs univariate and multivariate ARCH-LM tests for a VAR. This is a modification of vars::arch.test() for the class "varshrinkest".

Usage

arch.test_sh(x, lags.single = 16, lags.multi = 5,
  multivariate.only = TRUE)

Arguments

x	An object of class "varshrinkest" obtained by VARshrink()
lags.single	An integer of the lag order used for univariate ARCH statistics.
lags.multi	An integer of the lag order used for multivariate ARCH statistic.
multivariate.only	If TRUE, only the multivariate statistic is computed.

See Also

arch.test

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
arch.test_sh(estim)

---

Coefficient matrix

Description

Returns the estimated coefficients of a VAR(p) model as a matrix. This is a modification of vars::Bcoef() for the class "varshrinkest".

Usage

Bcoef_sh(x)

Arguments

x	An object of class "varshrinkest" generated by VARshrink().

Details

Consider VAR(p) model:

$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + C d_t + e_t .$

The function returns the concatenated matrix (A_1, ..., A_p, C) as a matrix object.

Value

A matrix holding the estimated coefficients of a VAR.

See Also

Bcoef

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
Bcoef_sh(estim)

---

BQ function for class "varshrinkest"

Description

This is a modification of vars::BQ() for the class "varshrinkest".

Usage

BQ_sh(x)

Arguments

x	An object of class "varshrinkest" obtained by VARshrink().

See Also

BQ

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
BQ_sh(estim)

---

Sum of squared errors (SSE) between coefficients of two VARs

Description

Compute sum of squared errors of coefficients of lagged endogenous variables (Acoef) of two VAR models.

Usage

calcSSE_Acoef(Acoef1, Acoef2)

Arguments

Acoef1, Acoef2

Each one is a list object with K-by-K coefficient matrices of lagged endogenous variables. See help(Acoef_sh), or, help(Acoef).

Details

Consider VAR(p) model:

$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + C d_t + e_t.$

The SSE of two VAR(p) models is expressed as

$sum_{k=1}^p sum_{i=1}^K sum_{j=1}^K ( (A_k)_{ij} - (A_k')_{ij} )^2.$

Value

SSE value.

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim1 <- VARshrink(y, p = 2, type = "const", method = "fbayes")
Acoef1 <- Acoef_sh(estim1)
estim2 <- VARshrink(y, p = 2, type = "const", method = "ridge")
Acoef2 <- Acoef_sh(estim2)
calcSSE_Acoef(Acoef1, Acoef2)

---

Causality Analysis for class "varshrinkest"

Description

A modification of vars::causality() for the class "varshrinkest".

Usage

causality_sh(x, cause = NULL, vcov. = NULL, boot = FALSE,
  boot.runs = 100)

Arguments

x	An object of class "varshrinkest" obtained by VARshrink().
cause, vcov., boot, boot.runs	Other arguments for causality analysis; see help(causality) for details.

See Also

causality

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
causality_sh(estim, cause = "e")

---

Convert format for VAR coefficients from Psi to varresult

Description

Convert a matrix of VAR coefficients estimated by a shrinkage method into a list of "shrinklm" object, where the class "shrinklm" inherits the class "lm".

Usage

convPsi2varresult(Psi, Y, X, lambda0, type = c("const", "trend", "both",
  "none"), ybar = NULL, xbar = NULL, Q_values = NULL, callstr = "")

Arguments

Psi	An M-by-K matrix of VAR coefficients
Y	An N-by-K data matrix of dependent variables
X	An N-by-M data matrix of regressors
lambda0	A rescaled shrinkage intensity parameter, based on which the effective number of parameters is computed by $Trace(X(X'X+lambda0*I)^{-1} X')$
type	Type of deterministic variables in the VAR estimation problem. Either of "const", "trend", "both", or "none".
ybar, xbar	NULL if Y and X are not centered. Mean vectors if Y and X had been centered. If Y and X had been centered (ybar and xbar are not NULL) and type is "const" or "both", then the coefficients for the constant term is computed and concatenated to the coefficients.
Q_values	Nonnegative weight vector of length N. Default is NULL. Take weights on rows (samples) of Y and X by sqrt(Q).
callstr	The call to VARshrink().

Details

Consider VAR(p) model:

$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + C d_t + e_t.$

It can be written in the matrix form:

$Y = X Psi + E,$

where Psi is a concatenated M-by-K matrix, Psi = (A_1, ..., A_p, C)^T. It can be written in the multiple linear regression form of a VAR(p) model:

$y_j = X psi_j + e_j, \quad j=1,...,K,$

where y_j, psi_j, and e_j are the j-th column vectors of Y, Psi, and E, respectively. This function converts Psi into a list of "shrinklm" objects, where each "shrinklm" object contains the length-M vector psi_j as coefficients.

Considering that each coefficient vector psi_j is estimated by a shrinkage method, the effective number of parameters, k_eff, is computed as:

$k_{eff} = Trace(X (X^T X + lambda0 * I)^{-1} X^T).$

Then, the degree of freedom of residuals is computed as:

$df.residual = N - k_{eff},$

where N is the number of rows of data matrices Y and X.

Value

A list object with objects of class c("shrinklm", "lm"). Each "shrinklm" object has components: coefficients, residuals, fitted.values, rank, df.residual, lambda0, call, terms, svd

---

Create coefficients of a VAR model

Description

Randomly create sparse lower-triangular matrices for VAR coefficients of lagged endogenous variables, and set a constant vector.

Usage

createVARCoefs_ltriangular(p = 1, K = 5, diag_val = 1/p,
  num_nonzero = 0, const_vector = NULL, range_min = 0.2,
  range_max = 1/p)

Arguments

p	lag order
K	Number of time series variables.
diag_val	diagonal values of A1,...,Ap
num_nonzero	Number of nonzero entries on the lower-triangular parts of A1, ..., Ap
const_vector	constant vector c of the VAR model
range_min, range_max	Each nonzero off-diagonal entry of coefficient matrices is drawn uniformly from the interval [-range_max, -range_min] U [range_min, range_max]

Details

Consider VAR(p) model:

$y_t = A_1 y_{t-1} + ... + A_p y_{t-p} + c + e_t,$

with the constant deterministic variable (d_t = 1). The function creates the coefficient matrices A_1, ..., A_p and constant vector c.

Diagonal elements of each K-by-K matrix A_k are all equal to diag_val, and off-diagonal elements are all zero except for a few randomly selected nonzero elements. Nonzero off-diagonal elements are selected from lower-triangular parts of A_i and the values are drawn from a uniform distribution over [-range_max, -range_min] U [range_min, range_max].

Value

A list object with components $A and $c. $A is a list of K-by-K matrices A_1, ..., A_p, and $c is a constant vector of length K.

Examples

p <- 1; K <- 20;
const_vector <- c(rep(0.2, 5), rep(0.7, 15))
createVARCoefs_ltriangular(p = p, K = K, diag_val = 0.6,
num_nonzero = K, const_vector = const_vector, range_max = 1)

---

Forecast Error Variance Decomposition

Description

Computes the forecast error variance decomposition of a VAR(p) for n.ahead steps. This is a modification of vars::fevd() for the class "varshrinkest".

Usage

## S3 method for class 'varshrinkest'
fevd(x, n.ahead = 10, ...)

Arguments

x	Object of class 'varshrinkest'; generated by VARshrink().
n.ahead	Integer specifying the steps.
...	Currently not used.

See Also

fevd

---

Impulse response function

Description

Computes the impulse response coefficients of a VAR(p) (or transformed VECM to VAR(p)) for n.ahead steps. This is a modification of vars::irf() for the class "varshrinkest".

Usage

## S3 method for class 'varshrinkest'
irf(x, impulse = NULL, response = NULL,
  n.ahead = 10, ortho = TRUE, cumulative = FALSE, boot = TRUE,
  ci = 0.95, runs = 100, seed = NULL, ...)

Arguments

x	Object of class 'varshrinkest'; generated by VARshrink()
impulse	A character vector of the impulses, default is all variables.
response	A character vector of the responses, default is all variables.
n.ahead	Integer specifying the steps.
ortho	Logical, if TRUE (the default) the orthogonalised impulse response coefficients are computed (only for objects of class 'varshrinkest').
cumulative	Logical, if TRUE the cumulated impulse response coefficients are computed. The default value is false.
boot	Logical, if TRUE (the default) bootstrapped error bands for the imuplse response coefficients are computed.
ci	Numeric, the confidence interval for the bootstrapped errors bands.
runs	An integer, specifying the runs for the bootstrap.
seed	An integer, specifying the seed for the rng of the bootstrap.
...	Currently not used.

See Also

irf

---

Full Bayesian Shrinkage Estimation Method for Multivariate Regression

Description

Estimate regression coefficients and scale matrix for noise by using Gibbs MCMC algorithm. The function assumes 1) multivariate t-distribution for noise as a sampling distribution, and 2) noninformative priors for regression coefficients and scale matrix for noise.

Usage

lm_full_Bayes_SR(Y, X, dof = Inf, burnincycle = 1000,
  mcmccycle = 2000)

Arguments

Y	An N x K matrix of dependent variables.
X	An N x M matrix of regressors.
dof	Degree of freedom for multivariate t-distribution. If dof = Inf (default), then multivariate normal distribution is applied and weight vector q is not estimated. If dof = NULL or dof <= 0, then dof and q are estimated automatically. If dof is a positive number, q is estimated.
burnincycle, mcmccycle	Number of burnin cycles is the number of initially generated sample values to drop. Number of MCMC cycles is the number of generated sample values to compute estimates.

Details

Consider the multivariate regression:

$Y = X Psi + e, \quad e ~ mvt(0, dof, Sigma).$

Psi is a M-by-K matrix of regression coefficients and Sigma is a K-by-K scale matrix for multivariate t-distribution for noise.

Sampling distribution for noise e is multivariate t-distribution with degree of freedom dof and scale matrix Sigma: e ~ mvt(0, dof, Sigma). The priors are noninformative priors: 1) the shrinkage prior for regression coefficients Psi, and 2) the reference prior for scale matrix Sigma.

The function implements Gibbs MCMC algorithm for estimating regression coefficients Psi and scale matrix Sigma.

Value

A list object with estimated parameters: Psi, Sigma, dof, delta (delta is the reciprocal of lambda), and lambda. Additional components are se.param (standard error of the parameters) and LINEXVARmodel (estimates under LINEX loss).

References

S. Ni and D. Sun (2005). Bayesian estimates for vector autoregressive models. Journal of Business & Economic Statistics 23(1), 105-117.

---

Multivariate Ridge Regression

Description

Estimate regression coefficients by using ridge regression.

Usage

lm_multiv_ridge(Y, X, lambda = 0, do_scale = FALSE)

Arguments

Y	An N x K matrix of dependent variables.
X	An N x M matrix of regressors.
lambda	Numeric vector of lambda values
do_scale	If true, X is centered and scaled, and Y is centered.

Details

Consider the multivariate regression:

$Y = X Psi + e.$

Psi is a M-by-K matrix of regression coefficients. The ridge regression estimate for the coefficients is

$Psi = (X'X + lambda * I)^{-1} X'Y.$

Value

A list object with the components: 1) Psi - A list of estimated Psi matrices, 2) lambda - A vector of lambda values, 3) GCV - A vector of GCV values

References

G. H. Golub, M. Heath, G. Wahba (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215-223. doi: 10.2307/1268518

---

Semiparametric Bayesian Shrinkage Estimation Method for Multivariate Regression

Description

Estimate regression coefficients and scale matrix for noise by using a parameterized cross validation (PCV). The function assumes 1) multivariate t-distribution for noise as a sampling distribution, and 2) informative priors for regression coefficients and scale matrix for noise.

Usage

lm_semi_Bayes_PCV(Y, X, dof = Inf, lambda = NULL, lambda_var = NULL,
  prior_type = c("NCJ", "CJ"), num_folds = 5, m0 = ncol(Y))

Arguments

Y	An N x K matrix of dependent variables.
X	An N x M matrix of regressors.
dof	Degree of freedom for multivariate t-distribution. If dof = Inf (default), then multivariate normal distribution is applied and weight vector q is not estimated. If dof = NULL or a numeric vector, then dof is selected by K-fold CV automatically and q is estimated.
lambda	If NULL or a vector of length >=2, it is selected by PCV.
lambda_var	If NULL, it is selected by a Stein-type shrinkage method.
prior_type	"NCJ" for non-conjugate prior and "CJ" for conjugate prior for scale matrix Sigma.
num_folds	Number of folds for PCV.
m0	A hyperparameter for inverse Wishart distribution for Sigma

Details

Consider the multivariate regression:

$Y = X Psi + e, \quad e ~ mvt(0, dof, Sigma).$

Psi is a M-by-K matrix of regression coefficients and Sigma is a K-by-K scale matrix for multivariate t-distribution for noise.

Sampling distribution for noise e is the multivariate t-distribution with degree of freedom dof and scale matrix Sigma: e ~ mvt(0, dof, Sigma). The priors are informative priors: 1) a shrinkage prior for regression coefficients Psi, and 2) inverse Wishart prior for scale matrix Sigma, which can be either non-conjugate ("NCJ") or conjugate ("CJ") to the shrinkage prior for coefficients Psi.

The function implements parameterized cross validation (PCV) for selecting a shrinkage parameter lambda for estimating regression coefficients (0 < lambda <= 1). In addition, the function uses a Stein-type shrinkage method for selecting a shrinkage parameter lambda_var for estimating variances of time series variables.

References

N. Lee, H. Choi, and S.-H. Kim (2016). Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise. Computational Statistics & Data Analysis 101, 250-276. doi: 10.1016/j.csda.2016.03.007

---

K-fold Cross Validation for Selection of Shrinkage Parameters of Semiparametric Bayesian Shrinkage Estimator for Multivariate Regression

Description

Estimate regression coefficients and scale matrix for noise by using semiparametric Bayesian shrinkage estimator, whose shrinkage parameters are selected by K-fold cross validation (KCV).

Usage

lm_ShVAR_KCV(Y, X, dof = Inf, lambda = NULL, lambda_var = NULL,
  prior_type = c("NCJ", "CJ"), num_folds = 5, m0 = ncol(Y))

Arguments

Y	An N x K matrix of dependent variables.
X	An N x M matrix of regressors.
dof	Degree of freedom for multivariate t-distribution. If dof = Inf (default), then multivariate normal distribution is applied and weight vector q is not estimated. If dof = NULL or a numeric vector, then dof is selected by K-fold CV automatically and q is estimated.
lambda	If NULL or a vector of length >=2, it is selected by KCV.
lambda_var	If NULL or a vector of length >=2, it is selected by KCV.
prior_type	"NCJ" for non-conjugate prior and "CJ" for conjugate prior for scale matrix Sigma.
num_folds	Number of folds for KCV.
m0	A hyperparameter for inverse Wishart distribution for Sigma

Details

The shrinkage parameters, lambda and lambda_var, for the semiparametric Bayesian shrinkage estimator are selected by KCV. See help(lm_semi_Bayes_PCV) for details about semiparametric Bayesian estimator.

References

N. Lee, H. Choi, and S.-H. Kim (2016). Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise. Computational Statistics & Data Analysis 101, 250-276. doi: 10.1016/j.csda.2016.03.007

---

Log-likelihood method for class "varshrinkest"

Description

Returns the log-likelihood of a VAR model estimated by VARshrink(). It extends vars::logLik.varest() to incorporate 1) multivariate t-distribution for residuals, 2) scale matrix Sigma provided by shrinkage methods, and 3) effective number of parameters provided by shrinkage methods.

Usage

## S3 method for class 'varshrinkest'
logLik(object, ...)

Arguments

object	An object of class "varshrinkest"
...	Currently not used.

Details

Acknowledgement: This code was contributed by Sung-Hoon Han & Dong-Han Lee @ Kangwon National University (2018.11.29.)

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
logLik(estim)

---

Normality, multivariate skewness and kurtosis test

Description

This function computes univariate and multivariate Jarque-Bera tests and multivariate skewness and kurtosis tests for the residuals of a VAR(p) or of a VECM in levels. This is a modification of vars::normality.test() for the class "varshrinkest".

Usage

normality.test_sh(x, multivariate.only = TRUE)

Arguments

x	An object of class "varshrinkest" obtained by VARshrink().
multivariate.only	If TRUE, only the multivariate statistics is computed.

See Also

normality.test

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
normality.test_sh(estim)

---

Coefficient matrices of the MA represention

Description

Returns the estimated coefficient matrices of the moving average representation of a stable VAR(p), of an SVAR as an array or a converted VECM to VAR. This is a modification of vars::Phi() for the class "varshrinkest".

Usage

## S3 method for class 'varshrinkest'
Phi(x, nstep = 10, ...)

Arguments

x	An object of class 'varshrinkest', generated by VARshrink().
nstep	An integer specifying the number of moving error coefficient matrices to be calculated.
...	Currently not used.

See Also

Phi

---

Predict method for objects of class varshrinkest

Description

Forecating a VAR object of class 'varshrinkest' with confidence bands. This is a modification of vars::predict.varest() for the class "varshrinkest".

Usage

## S3 method for class 'varshrinkest'
predict(object, ..., n.ahead = 10, ci = 0.95,
  dumvar = NULL)

Arguments

object	An object of class 'varshrinkest'; generated by VARshrink()
...	currently not used.
n.ahead	An integer specifying the number of forecast steps.
ci	The forecast confidence interval
dumvar	Matrix for objects of class ‘vec2var’ or ‘varest’, if the dumvar argument in ca.jo() has been used or if the exogen argument in VARshrink() has been used, respectively. The matrix should have the same column dimension as in the call to ca.jo() or to VARshrink() and row dimension equal to n.ahead.

---

Print method for class "varshrinkest"

Description

Print method for an object of class "varshrinkest"

Usage

## S3 method for class 'varshrinkest'
print(x, digits = max(3, getOption("digits") - 3),
  ...)

Arguments

x	An object of class "varshrinkest"
digits, ...	Other arguments for print() method

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
print(estim)

---

Print method for class "varshsum"

Description

Print method for an object obtained by summary.varshrinkest().

Usage

## S3 method for class 'varshsum'
print(x, digits = max(3, getOption("digits") - 3),
  signif.stars = getOption("show.signif.stars"), ...)

Arguments

x	An object of class "varshsum"
digits, signif.stars, ...	Other arguments for print(), printCoefmat(), format() method

Details

This function extends print.varsum() for VAR models estimated by shrinkage methods. The output includes scale matrix Sigma and degree of freedom dof for multivariate t-distribution for residuals.

---

Restricted VAR

Description

This is a modification of vars::restrict() for the class "varshrinkest". Warning: THIS CODE IS NOT COMPLETE: this function may raise an error because it ignores shrinkage estimation.

Usage

restrict_sh(x, ...)

Arguments

x	An object of class "varshrinkest"
...	Other arguments to vars::restrict()

See Also

restrict

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
restrict_sh(estim)

---

Eigenvalues of the companion coefficient matrix of a VAR(p)-process

Description

This is a variant of vars::roots() for an object of class 'varshrinkest', VAR parameters estimated by VARshrink().

Usage

roots_sh(x, modulus = TRUE)

Arguments

x	An object of class "varshrinkest"
modulus	TRUE for modulus of the roots.

See Also

roots

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
roots_sh(estim)

---

Test for serially correlated errors for VAR shrinkage estimate

Description

An extension of vars::serial.test() to the class "varshrinkest".

Usage

serial.test_sh(x, lags.pt = 16, lags.bg = 5,
  type = c("PT.asymptotic", "PT.adjusted", "BG", "ES"))

Arguments

x	An object of class "varshrinkest" obtained by VARshrink().
lags.pt, lags.bg, type	Other arguments for vars::serial.test(). see help(serial.test) for details.

See Also

serial.test

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
serial.test_sh(estim)

---

Semiparametric Bayesian Shrinkage Estimator for Multivariate Regression

Description

Compute the semiparametric Bayesian shrinkage estimator of Psi and Sigma for a given shrinkage parameter lambda. The function is a private function for lm_semi_Bayes_PCV() and lm_ShVAR_KCV().

Usage

shrinkVARcoef(Y, X, lambda, dof = Inf, prior_type = "NCJ",
  TolDRes = 1e-04, m0 = ncol(Y))

Arguments

Y	An N x K matrix of dependent variables.
X	An N x M matrix of regressors.
lambda	A shrinkage intensity parameter value between 0~1.
dof	Degree of freedom for multivariate t-distribution. If NULL or Inf, then use multivariate normal distribution.
prior_type	"NCJ" for non-conjugate prior and "CJ" for conjugate prior for scale matrix Sigma.
TolDRes	Tolerance parameter for stopping criterion.
m0	A hyperparameter for inverse Wishart distribution for Sigma

References

N. Lee, H. Choi, and S.-H. Kim (2016). Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise. Computational Statistics & Data Analysis 101, 250-276. doi: 10.1016/j.csda.2016.03.007

---

Generate multivariate time series data using the given VAR model

Description

Generate a multivariate time series data set using the given VAR model.

Usage

simVARmodel(numT, model, burnin = 0)

Arguments

numT	Number of observed time points, T.
model	A list object with Coef, Sigma, dof; Coef is a list with A and c; A is a list object of K-by-K coefficient matrices and c is a length-K vector. Sigma is a K-by-K scale matrix and dof is a degree of freedom for multivariate t-distribution for noise.
burnin	Number of initial points which are not included in the final values.

Details

First, it creates (p+burnin+numT x K) data, then it remove the first (p+burnin) vectors. Finally, it returns (numT x K) data.

Value

A numT-by-K matrix

Examples

myCoef <- list(A = list(matrix(c(0.5, 0, 0, 0.5), 2, 2)), c = c(0.2, 0.7))
myModel <- list(Coef = myCoef, Sigma = diag(0.1^2, 2), dof = Inf)
simVARmodel(numT = 100, model = myModel, burnin = 10)

---

Stability function

Description

A variant of vars::stability(). Warning: this function has not been tested for small sample sizes yet.

Usage

stability_sh(x, type = c("OLS-CUSUM", "Rec-CUSUM", "Rec-MOSUM",
  "OLS-MOSUM", "RE", "ME", "Score-CUSUM", "Score-MOSUM", "fluctuation"),
  h = 0.15, dynamic = FALSE, rescale = TRUE, ...)

Arguments

x	An object of class "varshrinkest"
type, h, dynamic, rescale, ...	Other arguments to strucchange::efp()

See Also

stability

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
stability_sh(estim)

---

Summary method for class "shrinklm"

Description

Class "shrinklm" inherits the class "lm", and it extends the "lm" class to incorporate shrinkage estimates with effective number of parameter.

Usage

## S3 method for class 'shrinklm'
summary(object, correlation = FALSE,
  symbolic.cor = FALSE, ...)

Arguments

object	An object of class "shrinklm"
correlation	If TRUE, the correlation matrix of the the estimated coefficients is returned and printed.
symbolic.cor	If TRUE, print the correlations in a symbolic form rather than as numbers
...	Currently not used.

---

Summary method for an object of class 'varshrinkest', VAR parameters estimated by VARshrink()

Description

Extend summary.varest() to class 'varshrinest' to incorporate adapted methods for new classes: summary.shrinklm(), logLik.varshrinkest(), roots.varshrinkest().

Usage

## S3 method for class 'varshrinkest'
summary(object, equations = NULL, ...)

Arguments

object	An object of class "varshrinkest", usually a result of call to "VARshrink()".
equations	Subset of names of endogenous time series variables to summarize.
...	Currently not used.

Details

Code is modified to avoid call to data matrices ($y, $datamat) and to use effective numbers of parameters of shrinkage estimates.

Output includes the scale matrix, Sigma, and degree-of-freedom, dof, for multivariate t-distribution for residuals.

Examples

data(Canada, package = "vars")
y <- diff(Canada)
estim <- VARshrink(y, p = 2, type = "const", method = "ridge")
summary(estim)

---

Shrinkage estimation of VAR parameters

Description

Shrinkage estimation methods for high-dimensional VAR models. Consider VAR(p) model: y_t = A_1 y_t-1 + ... + A_p y_t-p + C d_t + e_t, where y_t is K-dimensional time series, d_t is deterministic regressors, e_t is a noise process, and A_1, ..., A_p, and C are coefficient matrices. Exogenous variables can be included additionally as regressors.

Usage

VARshrink(y, p = 1, type = c("const", "trend", "both", "none"),
  season = NULL, exogen = NULL, method = c("ridge", "ns", "fbayes",
  "sbayes", "kcv"), lambda = NULL, lambda_var = NULL, dof = Inf, ...)

Arguments

y	A T-by-K matrix of endogenous variables
p	Integer for the lag order
type	Type of deterministic regressors to include. #' 1) "const" - the constant. 2) "trend" - the trend. 3) "both" - both the constant and the trend. 4) "none" - no deterministic regressors. ***Note: In the package version <= 0.3, method='ns' does not accept type="const" and type="both" to avoid constant term.
season	An integer value of frequency for inclusion of centered seasonal dummy variables. abs(season) >= 3.
exogen	A T-by-L matrix of exogenous variables. Default is NULL.
method	1) "ridge" - multivariate ridge regression. 2) "ns" - a Stein-type nonparametric shrinkage method. 3) "fbayes" - a full Bayesian shrinkage method using noninformative priors. 4) "sbayes" - a semiparametric Bayesian shrinkage method using parameterized cross validation. 5) "kcv" - a semiparametric Bayesian shrinkage method using K-fold cross validation
lambda, lambda_var	Shrinkage parameter value(s). Use of this parameter is slightly different for each method: the same value does not imply the same shrinkage estimates.
dof	Degree of freedom of multivariate t-distribution for noise. Valid only for method = "fbayes" and method = "sbayes". dof=Inf means multivariate normal distribution.
...	Extra arguments to pass to a specific function of the estimation method. For example, burnincycle and mcmccycle are for "fbayes".

Details

Shrinkage estimation methods can estimate the coefficients even when the dimensionality K is larger than the number of observations.

Value

An object of class "varshrinkest" with the components: varresult, datamat, y, type, p, K, obs, totobs, restrictions, method, lambda, call. The class "varshrinkest" inherits the class "varest" in the package vars.

Examples

data(Canada, package = "vars")
y <- diff(Canada)
VARshrink(y, p = 2, type = "const", method = "ridge")

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