Large.tVAR: Large.tVAR

In lucabarbaglia/t-VAR: Penalized Vector AutoRegressions with t-innovations

Description

ECM algorithm for the Large VAR with errors following a multivariate t-distribution with estimation of the degrees of freedom

Usage

Large.tVAR(
  Data_ECM,
  P,
  type_lasso = "Lasso",
  nu_init = NULL,
  maxit.ECM = 25,
  tol.ECM = 0.01,
  tol.nu = 0.001,
  maxit.both = 50,
  tol.both = 0.01,
  maxit.nu = 100,
  lambda1_min = NULL,
  lambda1_max = NULL,
  lambda1_steps = NULL,
  gamma1_min = NULL,
  gamma1_max = NULL,
  gamma1_steps = NULL,
  lambda1_OPT = NULL,
  gamma1_OPT = NULL
)

Arguments

Data_ECM	a NxJ matrix of log-volatilities. J: number of time series. N: time series length.
P	VAR order
type_lasso	type of lasso penalty. "Lasso" for standard lasso, "Group" for group lasso. Default is "Lasso".
nu_init	degrees-of-freedom initial value. Default is 1000.
maxit.ECM	maximum iterations for ECM algorithm. Default is 25.
tol.ECM	tolerance ECM algorithm. Default is 0.01.
maxit.both	maximum iterations for gaussian lasso algorithm. Default is 50.
tol.both	tolerance gaussian lasso algorithm. Default is 0.01.
maxit.nu	maximum iteration for estimation of the degrees-of-freedom. Default is 1000.
lambda1_min	minimum value of the regularization parameter on Beta. Default is NULL.
lambda1_max	maximum value of the regularization parameter on Beta. Default is NULL.
lambda1_steps	number of steps in the lambda grid. Default is NULL.
gamma1_min	minimum value of the regularization parameter on Omega. Default is NULL.
gamma1_max	maximum value of the regularization parameter on Omega. Default is NULL.
gamma1_steps	number of steps in the gamma grid. Default is NULL.
lambda1_OPT	optimal value of the regularization parameter on Beta. Default is NULL.
gamma1_OPT	optimal value of the regularization parameter on Omega. Default is NULL.

Value

A list containing:

"Beta_new"	a vector containing the estimated Beta.
"Beta_arr"	a JxJxP array containing the estimated Beta.
"innov"	a (N-P)xJ containing the estimated VAR residuals.
"Omega_new"	a JxJ matrix containing the estimated Omega.
"tau_new"	a vector of length N-P containing the estimated gamma variable tau.
"nu_new"	estimated degrees-of-freedom of the multivaraite t-distribution of the VAR innovations.
"Obj_ECM"	objective function.
"iter_ECM"	number of iterations of the ECM algorithm.
"iter_vec"	number of iteration of the Gaussian Lasso algorithm for each ECM iteration.
"lambda1_opt"	selected value of the regularization parameter on Beta.
"gamma1_opt"	selected value of the regularization parameter on Omega.

Author(s)

Luca Barbaglia https://lucabarbaglia.github.io/

References

Barbaglia, L., Croux, C., & Wilms, I. (2020). Volatility spillovers in commodity markets: A large t-vector autoregressive approach. Energy Economics, 85, 104555.

lucabarbaglia/t-VAR documentation built on Feb. 27, 2021, 3:46 a.m.