Mstep.hh.SCAD.MSAR: M step of the EM algorithm for fitting homogeneous...
In NHMSAR: Non-Homogeneous Markov Switching Autoregressive Models

Description Usage Arguments Details Value Author(s) References See Also

M step of the EM algorithm for fitting homogeneous multivariate Markov switching auto-regressive models with penalization of parameters of the VAR(1) models, called in fit.MSAR. Penalized maximum likelihood is used. Penalization may be add to the autoregressive matrices of order 1 and to the precision matrices (inverse of variance of innovation). Ridge, LASSO and SCAD penalization are implmented for the autoregressive matrices and only SCAD for the precision matrices.

1	Mstep.hh.SCAD.MSAR(data, theta, FB, lambda1=.1,lambda2=.1,penalty=,par=NULL)

`data`	array of univariate or multivariate series with dimension T x N.samples x d. T: number of time steps of each sample, N.samples: number of realisations of the same stationary process, d: dimension.
`theta`	model's parameter; object of class MSAR. See also init.theta.MSAR.
`FB`	Forward-Backward results, obtained by calling Estep.MSAR function
`lambda1`	penalization constant for the precision matrices. It may be a scalar or a vector of length M (with M the number of regimes). If it is equal to0 no penalization is introduced for the precision matrices.
`lambda2`	penalization constant for the autoregressive matrices. It may be a scalar or a vector of length M (with M the number of regimes). If it is equal to0 no penalization is introduced for the atoregression matrices.
`penalty`	choice of the penalty for the autoregressive matrices. Possible values are ridge, lasso or SCAD (default).
`par`	allows to give an initial value to the precision matrices.

When LASSO penalty is chosen, the LARS algorithm is used. When SCAD is chosen, a Newton-Raphson algorithm is run with a quadratic approximation of the penalized likelihood. For the precision matrices penalization, the package glasso is used.

Limit of this function: only works for VAR(1) models

`A0`	intercepts
`A`	AR coefficients
`sigma`	variance of innovation
`sigma.inv`	inverse of variance of innovation
`prior`	prior probabilities
`transmat`	transition matrix

Valerie Monbet, valerie.monbet@univ-rennes1.fr

Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al. (2004). Least angle regression. The Annals of statistics, 32(2):407-499.

Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96(456):1348-1360.

Mstep.hh.MSAR, fit.MSAR

NHMSAR documentation built on Feb. 9, 2022, 9:06 a.m.