BigVAR.fit {BigVAR}

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

Y

T \times k multivariate time series or Y T \times (k+m) endogenous and exogenous series, respectively

p

Predetermined maximal lag order (for modeled series)

struct

The choice of penalty structure (see details).

lambda

vector or matrix of penalty parameters.

alpha

grid of candidate parameters for the alpha in the Sparse Lag and Sparse Own/Other VARX-L

VARX

List containing VARX model specifications.

separate_lambdas

indicator for separate penalty parameters for each time series (default FALSE)

MN

Minnesota Prior Indicator

C

vector of coefficients to shrink toward a random walk (if MN is TRUE)

intercept

True or False: option to fit an intercept

tf

transfer function indicator (i.e. VARX in which p=0 & s>0) (default false)

tol

optimization tolerance (default 1e-4)

RVAR

True or False: option to refit based upon the support selected using the Relaxed-VAR procedure

refit_fraction

fraction of least squares refit to incorporate (default 1)

beta

optional k\times (k\times p + m\times s +1) coefficient matrix to use as a 'warm start' (default NULL)

gamma

additional parameter for SCAD/MCP penalty (default 3)

@details The choices for 'struct' are as follows

• 'Basic' (Basic VARX-L)

• 'BasicEN' (Basic 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 (cf. Breheny and Huang))

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

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', '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)