regsc_ic {regsc}R Documentation

Estimate the regression with structural changes by the group fused Lasso

Description

Estimate the regression with structural changes, using information criterion (IC) to determine the tuning parameter on the group-fused-Lasso penalty.

Usage

regsc_ic(y,x,z=numeric(0),S=20,h=1,weight=rep(1,length(y)-1),XTol=1e-6,maxIter=1000)

Arguments

y

An n-by-1 numeric matrix (vector), the dependent variable

x

An n-by-p numeric matrix, the regressors with possibly time-varying effect on y

z

An optional n-by-q numeric matrix, the regressors with time-invariant effect on y

S

An optional positive integer, the number of grids for the search for the optimal tuning parameter.

h

An optional positive number, used in the determination of break dates.

weight

An optional (n-1)-by-1 numeric vector

XTol

An optional small number, the level of error tolerance

maxIter

An optional integer, the maximum number of iterations allowed

Value

A list of post-Lasso estimation result: regime,alpha, Sigma, ssr, R2, resid, lambda, L, IC, K, listRegime.

regime

a (m+2)-by-1 numeric vector, containing {1,T1,...,Tm,n+1}, where T1,...,Tm are m breaks

alpha

a (p*(m+1)+q)-by-1 vector of estimated coefficients.The first p*(m+1) elements of alpha correspond to the time-varying effects of x on y. For example, alpha[1:p] is the estimated coefficient on x in the first regime.

Sigma

the estimated covariance matrix for alpha

ssr

the sum of squared residuals

R2

the overall goodness-of-fit

resid

an n-by-1 vector of the fitted residual

lambda

the selected tuning parameter that minimizes IC.

L

a numeric vector in ascending order, each element of which is a candidate for the tuning parameter lambda

IC

a numeric vector of calculated information criteria corresponding to different values of the tuning parameter in L

K

a vector of integers, each of which is the number of breaks corresponding to different values of the tuning parameter in L

listRegime

a list of vectors, each of which is the estimated regime corresponding different values of the tuning parameter in L

Note that the repetitive elements of L, IC, K, listRegime are deleted.

Author(s)

Junhui Qian and Liangjun Su

References

Qian, J., L. Su, 2016, "Shrinkage estimation of regression models with multiple structural changes", Econometric Theory, 32 (6), 1376-1433.

See Also

regsc


[Package regsc version 0.3 Index]