EM_VAR: EM_VAR

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

Description

EM algorithm for the Robust Sparse VAR with errors following a multivariate t-distribution (without estimation of df)

Usage

EM_VAR(
  Data_EM,
  P,
  type_lasso = "Lasso",
  nu,
  maxit.EM = 25,
  tol.EM = 0.01,
  maxit.both = 50,
  tol.both = 0.01,
  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_EM	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	degrees-of-freedom of the multivaraite t-distribution of the VAR innovations.
maxit.EM	maximum iterations for EM algorithm. Default is 25.
tol.EM	tolerance EM 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.
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.
"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.