par.lrpc {fnets}

Parametric estimation of long-run partial correlations of factor-adjusted VAR processes

Description

Returns a parametric estimate of long-run partial correlations of the VAR process from the VAR parameter estimates and the inverse of innovation covariance matrix obtained via constrained l1-minimisation.

Usage

par.lrpc(
  object,
  eta = NULL,
  tuning.args = list(n.folds = 1, path.length = 10),
  lrpc.adaptive = FALSE,
  eta.adaptive = NULL,
  do.correct = TRUE,
  do.threshold = FALSE,
  n.cores = 1
)

Arguments

object

fnets object

eta

l1-regularisation parameter; if eta = NULL, it is selected by cross validation

tuning.args

a list specifying arguments for the cross validation procedure for selecting the tuning parameter involved in long-run partial correlation matrix estimation. It contains:

n.folds

positive integer number of folds

path.length

positive integer number of regularisation parameter values to consider; a sequence is generated automatically based in this value

lrpc.adaptive

whether to use the adaptive estimation procedure

eta.adaptive

l1-regularisation parameter for Step 1 of the adaptive estimation procedure; if eta.adaptive = NULL, the default choice is 2 * sqrt(log(dim(x)[1])/dim(x)[2])

do.correct

whether to correct for any negative entries in the diagonals of the inverse of long-run covariance matrix

do.threshold

whether to perform adaptive thresholding of Delta and Omega parameter estimators with threshold

n.cores

number of cores to use for parallel computing, see makePSOCKcluster

Details

See Barigozzi, Cho and Owens (2024+) for further details, and Cai, Liu and Zhou (2016) for further details on the adaptive estimation procedure.

Value

a list containing

Delta

estimated inverse of the innovation covariance matrix

Omega

estimated inverse of the long-run covariance matrix

pc

estimated innovation partial correlation matrix

lrpc

estimated long-run partial correlation matrix

eta

l1-regularisation parameter

lrpc.adaptive

input argument

References

Barigozzi, M., Cho, H. & Owens, D. (2024+) FNETS: Factor-adjusted network estimation and forecasting for high-dimensional time series. Journal of Business & Economic Statistics (to appear).

Cai, T. T., Liu, W., & Zhou, H. H. (2016) Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation. The Annals of Statistics, 44(2), 455-488.

Owens, D., Cho, H. & Barigozzi, M. (2024+) fnets: An R Package for Network Estimation and Forecasting via Factor-Adjusted VAR Modelling. The R Journal (to appear).

Examples

out <- fnets(data.unrestricted, do.lrpc = FALSE, var.args = list(n.cores = 2))
plrpc <- par.lrpc(out, n.cores = 2)
out$lrpc <- plrpc
out$do.lrpc <- TRUE
plot(out, type = "pc", display = "network")
plot(out, type = "lrpc", display = "heatmap")