Generator for Simulated Multivariate Time Series

Description

Coefficient matrix for a stationary simulated multivariate time series

Details

Example generator matrix adapted from Table 3.2 of Gredenhoff and Karlsson (1997)

Author(s)

Will Nicholson

References

Gredenhoff, Mikael, and Sune Karlsson. "Lag-length selection in VAR-models using equal and unequal lag-length procedures." Computational Statistics 14.2 (1999): 171-187.

Dimension Reduction Methods for Multivariate Time Series.

Description

BigVAR implements the HLAG and VARX-L frameworks which allow for the estimation of vector autoregressions and vector autoregressions with exogenous variables using structured convex penalties. This package originated as a 2014 Google "Summer of Code" Project. The development version of this package is hosted on github: https://github.com/wbnicholson/BigVAR.

Details

To use the facilities of this package, starting with an T \times k+m multivariate time series (in which T denotes the length of the series, k the number of endogenous or "model") and run constructModel to create an object of class BigVAR. cv.BigVAR creates an object of class BigVAR.results, which chooses an optimal penalty parameter based on minimizing h-step ahead forecasts on a specified cross-validation period over a grid of values as well as comparisons against AIC, BIC, unconditional mean, and a random walk. There are plot functions for both BigVAR (plot.BigVAR) and BigVAR.results (plot) as well as a predict function for BigVAR.results (predict).

Author(s)

Will Nicholson wbn8@cornell.edu,

References

Lutkepohl "New Introduction to Multivariate Time Series", Banbura, Marta, Domenico Giannone, and Lucrezia Reichlin. 'Large Bayesian vector auto regressions.' Journal of Applied Econometrics 25.1 (2010): 71-92. Breheny P, Huang J (2011). “Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection.” Annals of Applied Statistics, 5(1), 232–253. Nicholson, William, I. Wilms, J. Bien, and D. S. Matteson. High dimensional forecasting via interpretable vector autoregression. Journal of Machine Learning Research, 21(166):1–52, 2020. William B. Nicholson, David S. Matteson, Jacob Bien,VARX-L: Structured regularization for large vector autoregressions with exogenous variables, International Journal of Forecasting, Volume 33, Issue 3, 2017, Pages 627-651, William B Nicholson, David S. Matteson, and Jacob Bien (2016), 'BigVAR: Tools for Modeling Sparse High-Dimensional Multivariate Time Series' arxiv:1702.07094

See Also

constructModel, cv.BigVAR, BigVAR.results, plot, predict

Examples

# Fit a Basic VAR-L(3,4) on simulated data
data(Y)
T1=floor(nrow(Y)/3)
T2=floor(2*nrow(Y)/3)
m1=constructModel(Y,p=4,struct="Basic",gran=c(50,10),verbose=FALSE,T1=T1,T2=T2,IC=FALSE)
plot(m1)
results=cv.BigVAR(m1)
plot(results)
predict(results,n.ahead=1)

BigVAR Object Class

Description

An object class to be used with cv.BigVAR

Details

To construct an object of class BigVAR, use the function constructModel

Slots

Data

a T \times k multivariate time series

model_data

processed time series and lag matrix

lagmax

Maximal lag order for modeled series

intercept

Indicator as to whether an intercept should be included

Structure

Penalty Structure

Relaxed

Indicator for relaxed VAR

Granularity

Granularity of penalty grid

horizon

Desired Forecast Horizon

crossval

Cross-Validation Procedure

Minnesota

Minnesota Prior Indicator

verbose

Indicator for Verbose output

dates

dates extracted from an xts object

ic

Indicator for including AIC and BIC benchmarks

VARX

VARX Model Specifications

VARXI

VARX Indicator

T1

Index of time series in which to start cross validation

T2

Index of times series in which to start forecast evaluation

ONESE

Indicator for 'One Standard Error Heuristic'

ownlambdas

Indicator for user-supplied lambdas

tf

Indicator for transfer function

alpha

Grid of candidate alpha values (applies only to Sparse VARX-L and Elastic Net models)

recursive

Indicator as to whether recursive multi-step forecasts are used (applies only to multiple horizon VAR models)

constvec

vector indicating variables to shrink toward a random walk instead of toward zero (valid only if Minnesota is TRUE)

tol

optimization tolerance

window.size

size of rolling window. If set to NULL an expanding window will be used.

separate_lambdas

indicator to use separate penalty parameter for each time series (default FALSE)

loss

Loss function to select penalty parameter (one of 'L1','L2','Huber').

delta

delta parameter for Huber loss (default 2.5)

gamma

gamma parameter for SCAD or MCP penalty (default 3)

rolling_oos

True or False: indicator to update the penalty parameter over the evaluation period (default False)

linear

indicator for linearly decrementing penalty grid (FALSE is log-linear).

refit_fraction

fraction of least squares refit to incorporate (default is 1).

See Also

constructModel

BigVAR Estimation

Description

Fit a BigVAR object with a structured penalty (VARX-L or HLAG).

Usage

BigVAR.est(object)

Arguments

Details

Fits HLAG or VARX-L model on a BigVAR object. Does not perform cross-validation. This method allows the user to construct their own penalty parameter selection procedure.

Value

An array of k \times kp \times n or k\times kp+ms \times n coefficient matrices; one for each of the n values of lambda.

See Also

constructModel, BigVAR.results,cv.BigVAR

Examples

data(Y)
Y=Y[1:100,]
#construct a Basic VAR-L
Model1=constructModel(Y,p=4,struct='Basic',gran=c(50,10))
BigVAR.est(Model1)

Simple function to fit BigVAR model with fixed penalty parameter

Description

Simple function to fit BigVAR model with fixed penalty parameter

Usage

BigVAR.fit(
  Y,
  p,
  struct,
  lambda,
  alpha = NULL,
  VARX = list(),
  separate_lambdas = F,
  MN = F,
  C = as.double(NULL),
  intercept = TRUE,
  tf = F,
  tol = 1e-04,
  RVAR = F,
  refit_fraction = 1,
  beta = NULL,
  gamma = 3
)

Arguments

Note

The specifications 'Basic', 'Lag,' 'SparseLag,' 'SparseOO,' and 'OwnOther' can accommodate both VAR and VARX models. EFX only applies to VARX models. 'HLAGC,' 'HLAGOO,' 'HLAGELEM,' and 'Tapered' can only be used with VAR models. Our implementation of the SCAD and MCP penalties is heavily influenced by the implementation in ncvreg.

References

Banbura, Marta, Domenico Giannone, and Lucrezia Reichlin. 'Large Bayesian vector auto regressions.' Journal of Applied Econometrics 25.1 (2010): 71-92. Breheny P, Huang J (2011). “Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection.” Annals of Applied Statistics, 5(1), 232–253. William B Nicholson, Jacob Bien, and David S Matteson. 'High Dimensional Forecasting via Interpretable Vector Autoregression.' arXiv preprint arXiv:1412.5250, 2016. William B. Nicholson, David S. Matteson, Jacob Bien,VARX-L: Structured regularization for large vector autoregressions with exogenous variables, International Journal of Forecasting, Volume 33, Issue 3, 2017, Pages 627-651, William B Nicholson, David S. Matteson, and Jacob Bien (2016), 'BigVAR: Tools for Modeling Sparse High-Dimensional Multivariate Time Series' arxiv:1702.07094

See Also

cv.BigVAR,BigVAR.est,constructModel

Examples

# VARX Example
# Fit a Basic VARX-L with k=2, m=1, s=2, p=4, lambda=1e-2
VARX <- list()
VARX$k <- 2 # indicates that the first two series are modeled
VARX$s <- 2 # sets 2 as the maximal lag order for exogenous series
data(Y)
BigVAR.fit(Y, p = 4, "Basic", lambda = 1e-2, VARX = VARX)

BigVAR.intermediate This class contains the in-sample results for cv.BigVAR

Description

It inherits the class BigVAR, and contains the results from rolling validation

Fields

ZFull

List containing full lag matrix and time series

InSampMSFE

In-sample MSFE from optimal value of lambda

LambdaGrid

Grid of candidate lambda values

index

Index order of optimal lambda value

OptimalLambda

Value of lambda that minimizes MSFE

Data

a T \times k or T\times k + m multivariate time Series

lagmax

Maximal lag order

Structure

Penalty structure

Relaxed

Indicator for relaxed VAR

Granularity

Granularity of penalty grid

horizon

Desired forecast horizon

crossval

Cross-Validation procedure

alpha

additional penalty parameter for Sparse Lag Group or Sparse Own/Other methods. Will contain either the heuristic choice of 1/(k+1) or the value selected by cross validation if the argument dual is set to TRUE

Minnesota

Minnesota Prior Indicator

verbose

verbose indicator

dual

indicator as to whether dual cross validation was conducted

contemp

indicator if contemporaneous exogenous predictors are used

Note

One can also access any object of class BigVAR from BigVAR.intermediate

Author(s)

Will Nicholson

BigVAR.results This class contains the results from cv.BigVAR.

Description

It inherits the class BigVAR, but contains substantially more information.

Fields

InSampMSFE

In-sample MSFE from optimal value of lambda

LambdaGrid

Grid of candidate lambda values

index

Rank of optimal lambda value

OptimalLambda

Value of lambda that minimizes MSFE

OOSMSFE

Average Out of sample MSFE of BigVAR model with optimal lambda

seoosfmsfe

Standard error of out of sample MSFE of BigVAR model with optimal lambda

MeanMSFE

Average out of sample MSFE of unconditional mean forecast

MeanSD

Standard error of out of sample MSFE of unconditional mean forecast

MeanPreds

predictions from conditional mean model

RWMSFE

Average out of sample MSFE of random walk forecast

RWPreds

Predictions from random walk model

RWSD

Standard error of out of sample MSFE of random walk forecast

AICMSFE

Average out of sample MSFE of AIC forecast

AICSD

Standard error of out of sample MSFE of AIC forecast

AICPreds

Predictions from AIC VAR/VARX model

AICpvec

Lag orders selected from AIC VAR model

AICpvec

Lag orders selected from AIC VARX model

BICMSFE

Average out of sample MSFE of BIC forecast

BICSD

Standard error of out of sample MSFE of BIC forecast

BICPreds

Predictions from BIC VAR/VARX model

BICpvec

Lag orders selected from BIC VAR model

BICpvec

Lag orders selected from BIC VARX model

betaPred

The final estimated k\times kp+ms+1 coefficient matrix, to be used for prediction

Zvals

The final lagged values of Y, to be used for prediction

fitted

fitted values obtained from betaPred

resids

residuals obtained from betaPred

Data

a T \times k or T\times k + m multivariate time Series

lagmax

Maximal lag order

Structure

Penalty structure

Relaxed

Indicator for relaxed VAR

Granularity

Granularity of penalty grid

horizon

Desired forecast horizon

crossval

Cross-Validation procedure

alpha

additional penalty parameter for Sparse Lag Group or Sparse Own/Other methods. Will contain either the heuristic choice of 1/(k+1) or the value selected by cross validation if the argument dual is set to TRUE

VARXI

VARX Indicator

Minnesota

Minnesota Prior Indicator

verbose

verbose indicator

dual

indicator as to whether dual cross validation was conducted

contemp

indicator if contemporaneous exogenous predictors are used

lagmatrix

matrix of lagged values used to compute residuals (of which Zvals is the final column)

betaArray

array of VAR/VARX coefficients from out of sample forecasts

sparse_count

average fraction of active coefficients in validation period

lambda_evolve_path

evolution of lambda over evaluation period

Note

One can also access any object of class BigVAR from BigVAR.results

Author(s)

Will Nicholson

Simulate a VAR

Description

Simulate a VAR

Usage

MultVarSim(k, A1, p, Sigma, T)

Arguments

Value

Returns a T \times k of realizations from a VAR.

References

Lutkepohl, 'A New Introduction to Multiple Time Series Analysis'

See Also

VarptoVar1MC

Examples

k=3;p=6
B=matrix(0,nrow=k,ncol=p*k)
A1<- matrix(c(.4,-.02,.01,-.02,.3,.02,.01,.04,.3),ncol=3,nrow=3)
A2 <- matrix(c(.2,0,0,0,.3,0,0,0,.13),ncol=3,nrow=3)
B[,1:k]=A1
B[,(4*k+1):(5*k)]=A2
A <- VarptoVar1MC(B,p,k)
Y <-MultVarSim(k,A,p,.1*diag(k),100)

One-step ahead predictions for VARX models

Description

One-step ahead predictions for VARX models

Usage

PredictVARX(VARXRes)

Arguments

Value

Returns a vector consisting of the out-of-sample forecasts for the provided VARXFit model.

See Also

VARXFit

Examples

data(Y)
# fit a VAR_3(3)
mod <- VARXFit(Y,3,NULL,NULL)
pred <-PredictVARX(mod)

Sparsity Plot of a BigVAR.results object

Description

Sparsity Plot of a BigVAR.results object

Usage

SparsityPlot.BigVAR.results(object)

Arguments

Details

Uses levelplot from the lattice package to plot the magnitude of each coefficient in the last coefficient estimated by cv.BigVAR.

Value

NA, side effect is graph

See Also

cv.BigVAR, BigVAR.results

Examples

data(Y)
Y <- Y[1:100,]
Model1 <- constructModel(Y,p=4,struct='Basic',gran=c(50,10),verbose=FALSE)
SparsityPlot.BigVAR.results(cv.BigVAR(Model1))

Fit a VAR or VARX model by least squares

Description

Fit a VAR or VARX model by least squares

Usage

VARXFit(Y, p, IC, VARX = NULL)

Arguments

Details

This function uses a modified form of the least squares technique proposed by Neumaier and Schneider (2001). It fits a least squares VAR or VARX via a QR decomposition that does not require explicit matrix inversion. This results in improved computational performance as well as numerical stability over the conventional least squares approach.

Value

Returns a list with four entries:

References

Neumaier, Arnold, and Tapio Schneider. 'Estimation of parameters and eigenmodes of multivariate autoregressive models.' ACM Transactions on Mathematical Software (TOMS) 27.1 (2001): 27-57.

See Also

constructModel, cv.BigVAR,BigVAR.fit

Examples

data(Y)
# fit a VAR_3(3)
mod <- VARXFit(Y,3,NULL,NULL)
# fit a VAR_3 with p= 6 and lag selected according to AIC
modAIC <- VARXFit(Y,6,'AIC',NULL)
# Fit a VARX_{2,1} with p=6, s=4 and lags selected by BIC
modXBIC <- VARXFit(Y,6,'BIC',list(k=1,s=4))

Evaluate forecasts from a VAR or VARX with lag orders selected by AIC/BIC

Description

Evaluate forecasts from a VAR or VARX with lag orders selected by AIC/BIC

Usage

VARXForecastEval(
  Y,
  X,
  p,
  s,
  T1,
  T2,
  IC,
  h,
  iterated = FALSE,
  loss = "L2",
  delta = 2.5
)

Arguments

Details

This function evaluates the one-step ahead forecasts of a VAR or VARX fit by least squares over an evaluation period. At every point in time, lag orders for the endogenous and exogenous series are selected according to AIC or BIC. This function is run automatically when cv.BigVAR is called unless ic is set to FALSE in constructModel.

Value

Returns the one-step ahead MSFE as well as the forecasts over the evaluation period and lag order selected.

References

Neumaier, Arnold, and Tapio Schneider. 'Estimation of parameters and eigenmodes of multivariate autoregressive models.' ACM Transactions on Mathematical Software (TOMS) 27.1 (2001): 27-57.

See Also

VARXFit,constructModel, cv.BigVAR

Examples

data(Y)

# Evaluate the performance of a VAR with lags selected by BIC.
p <- 4
T1 <- floor(nrow(Y))/3
T2 <- floor(2*nrow(Y))/3
# Matrix of zeros for X
X <- matrix(0,nrow=nrow(Y),ncol=ncol(Y))
BICMSFE <- VARXForecastEval(Y,X,p,0,T1,T2,'BIC',1)

Construct a VAR or VARX lag matrix

Description

Construct a VAR or VARX lag matrix

Usage

VARXLagCons(Y, X = NULL, p, s = 0, oos = FALSE, contemp = FALSE)

Arguments

Details

This function is not required unless you which to design your own cross validation routine.

Value

list with two entries:

References

See page 15 of Lutkepohl, 'A New Introduction to Multiple Time Series Analysis

See Also

MultVarSim

Examples

data(Y)
# construct VAR lag matrix with p=4
ZZ<-VARXLagCons(Y,X=NULL,p=4,s=0)

Converts a VAR coefficient matrix of order p to multiple companion form

Description

Converts a VAR coefficient matrix of order p to multiple companion form

Usage

VarptoVar1MC(B, p, k)

Arguments

Value

Returns a kp \times kp coefficient matrix representing all coefficient matrices contained in Ai as a VAR(1).

References

See page 15 of Lutkepohl, 'A New Introduction to Multiple Time Series Analysis'

See Also

MultVarSim

Examples

k=3;p=6
B=matrix(0,nrow=k,ncol=p*k)
A1<- matrix(c(.4,-.02,.01,-.02,.3,.02,.01,.04,.3),ncol=3,nrow=3)
A2 <- matrix(c(.2,0,0,0,.3,0,0,0,.13),ncol=3,nrow=3)
B[,1:k]=A1
B[,(4*k+1):(5*k)]=A2
A <- VarptoVar1MC(B,p,k)

Simulated Multivariate Time Series

Description

Realization of a simulated multivariate time series

Details

100 \times 3 multivariate time series distributed according to the generator matrix A.

Author(s)

Will Nicholson

Example quarterly macroeconomic data

Description

Example multivariate macroeconomic time series

Details

US Macroeconomic Time Series: CPI, Federal Funds Rate, Gross Domestic Product, and M1. Ranging from Q2 1959 to Q1 2025. Procured from FRED, Federal Reserve Bank of St. Louis.

Author(s)

Will Nicholson

Default coef method BigVAR-results, returns the last coefficient matrix from the evaluation period

Description

Default coef method BigVAR-results, returns the last coefficient matrix from the evaluation period

Usage

## S4 method for signature 'BigVAR.results'
coef(object)

Arguments

Details

displays formatted coefficient matrix

Construct an object of class BigVAR

Description

Construct an object of class BigVAR

Usage

constructModel(
  Y,
  p,
  struct,
  gran,
  h = 1,
  cv = "Rolling",
  verbose = TRUE,
  IC = TRUE,
  VARX = list(),
  T1 = floor(nrow(Y)/3),
  T2 = floor(2 * nrow(Y)/3),
  ONESE = FALSE,
  ownlambdas = FALSE,
  recursive = FALSE,
  dates = as.character(NULL),
  window.size = 0,
  separate_lambdas = FALSE,
  linear = FALSE,
  loss = "L2",
  rolling_oos = FALSE,
  model.controls = list()
)

Arguments

Details

The choices for 'struct' are as follows

• 'Basic' (Basic VARX-L)

• 'BasicEN' (Elastic Net VARX-L)

• 'Lag' (Lag Group VARX-L)

• 'SparseLag' (Lag Sparse Group VARX-L)

• 'OwnOther' (Own/Other Group VARX-L)

• 'SparseOO' (Own/Other Sparse Group VARX-L)

• 'EFX' (Endogenous First VARX-L)

• 'HLAGC' (Componentwise HLAG)

• 'HLAGOO' (Own/Other HLAG)

• 'HLAGELEM' (Elementwise HLAG)

• 'Tapered' (Lag weighted Lasso VAR)

• 'BGR' (Bayesian Ridge Regression (cf. Banbura et al))

• 'MCP' (Minimax Concave Penalty (cf. Breheny and Huang))

• 'SCAD' (Smoothly Clipped Absolute Deviation Penalty (cf. Breheny and Huang))

The first number in the vector 'gran' specifies how deep to construct the penalty grid and the second specifies how many penalty parameters to use If ownlambas is set to TRUE, gran should contain the user-supplied penalty parameters.

VARX specifications consist of a named list with entry k denoting the series that are to be modeled and entry s to denote the maximal lag order for exogenous series.

As the capabilities of BigVAR have expanded, we have decided to consolidate parameters in the list model.controls. These parameters include:

• 'alpha:' grid of candidate parameters for the alpha in the Basic Elastic Net, Sparse Lag, Sparse Own/Other VARX-L.

• 'C:' vector of coefficients to shrink toward a random walk (if MN is TRUE).

• 'delta:' parameter for Huber loss (default 2.5)

• 'intercept:' option to fit an intercept, default TRUE

• 'loss:' Loss function to select penalty parameter (one of 'L1','L2','Huber')

• 'MN:' Minnesota Prior Indicator, default FALSE

• 'RVAR:' option to refit based upon the support selected using the Relaxed-VAR procedure (default FALSE).

• 'refit_fraction:' If RVAR is TRUE, proportional tradeoff between least squares fit and penalized fit (default 1).

• 'tol:' optimization tolerance (default 1e-4)

The argument alpha is ignored unless the structure choice is 'SparseLag' or 'Lag.' By default 'alpha' is set to NULL and will be initialized as 1/(k+1) in cv.BigVAR and BigVAR.est. Any user supplied values must be between 0 and 1.

Note

The specifications 'Basic','BasicEN', 'Lag,' 'SparseLag,' 'SparseOO','OwnOther', 'MCP', and 'SCAD.' can accommodate both VAR and VARX models. EFX only applies to VARX models. 'HLAGC,' 'HLAGOO,' 'HLAGELEM,' and 'Tapered' can only be used with VAR models. Our implementation of the SCAD and MCP penalties is heavily influenced by the package ncvreg.

References

Banbura, Marta, Domenico Giannone, and Lucrezia Reichlin. 'Large Bayesian vector auto regressions.' Journal of Applied Econometrics 25.1 (2010): 71-92. Breheny P, Huang J (2011). “Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection.” Annals of Applied Statistics, 5(1), 232–253. Nicholson, William, I. Wilms, J. Bien, and D. S. Matteson. High dimensional forecasting via interpretable vector autoregression. Journal of Machine Learning Research, 21(166):1–52, 2020. William B. Nicholson, David S. Matteson, Jacob Bien,VARX-L: Structured regularization for large vector autoregressions with exogenous variables, International Journal of Forecasting, Volume 33, Issue 3, 2017, Pages 627-651, William B Nicholson, David S. Matteson, and Jacob Bien (2016), 'BigVAR: Tools for Modeling Sparse High-Dimensional Multivariate Time Series' arxiv:1702.07094

See Also

cv.BigVAR,BigVAR.est

Examples

# VARX Example
# Create a Basic VARX-L with k=2, m=1, s=2, p=4
VARX=list()
VARX$k=2 # indicates that the first two series are modeled
VARX$s=2 # sets 2 as the maximal lag order for exogenous series
data(Y)
T1=floor(nrow(Y)/3)
T2=floor(2*nrow(Y)/3)
Model1=constructModel(Y,p=4,struct='Basic',gran=c(50,10),verbose=FALSE,VARX=VARX,T1=T1,T2=T2)

Cross Validation for BigVAR

Description

Cross Validation for BigVAR

Usage

cv.BigVAR(object)

Arguments

Details

The main function of the BigVAR package. Performs cross validation to select penalty parameters over a training sample (as the minimizer of in-sample MSFE), then evaluates them over a test set. Compares against sample mean, random walk, AIC, and BIC benchmarks. Creates an object of class BigVAR.results

Value

An object of class BigVAR.results.

See Also

constructModel, BigVAR.results,BigVAR.est

Examples

data(Y)
# Fit a Basic VARX-L with rolling cross validation 
Model1=constructModel(Y,p=4,struct='Basic',gran=c(50,10), verbose=FALSE)
results=cv.BigVAR(Model1)

Plot an object of class BigVAR.results

Description

Plot an object of class BigVAR.results

Usage

## S4 method for signature 'BigVAR.results'
plot(x, y = NULL, ...)

Arguments

Details

Plots the in sample MSFE of all values of lambda with the optimal value highlighted.

Plot a BigVAR object

Description

Plot a BigVAR object

Usage

## S4 method for signature 'BigVAR'
plot(x, y = NULL, ...)

Arguments

Details

Uses plot.zoo to plot each indivdual series of Y on a single plot

Value

NA, side effect is graph

See Also

constructModel

Forecast using a BigVAR.results object

Description

Forecast using a BigVAR.results object

Usage

predict(object,...)

Arguments

Details

Provides n.ahead step forecasts using the model produced by cv.BigVAR. If confint is set to TRUE, a 95 percent confidence interval will also be returned.

See Also

cv.BigVAR

Examples

data(Y)
Y=Y[1:100,]
Model1=constructModel(Y,p=4,struct='Basic',gran=c(50,10),verbose=FALSE)
results=cv.BigVAR(Model1)
predict(results,n.ahead=1)

Default show method for an object of class BigVAR.results

Description

Default show method for an object of class BigVAR.results

Usage

## S4 method for signature 'BigVAR.results'
show(object)

Arguments

Details

prints forecast results and additional diagnostic information as well as comparisons with mean, random walk, and AIC, and BIC benchmarks

See Also

cv.BigVAR,BigVAR.results

Default show method for an object of class BigVAR

Description

Default show method for an object of class BigVAR

Usage

## S4 method for signature 'BigVAR'
show(object)

Arguments

Value

Displays the following information about the BigVAR object:

• Prints the first 5 rows of Y

• Penalty Structure

• Relaxed Least Squares Indicator

• Maximum lag order

• VARX Specifications (if applicable)

• Start, end of cross validation period

See Also

constructModel