Breg: Regularize Bayesian predictive regression

In Jianeng/FinReg: Regularizing Bayesian Predictive Regressions

Description

Given regularization parameters, this function uses an iterative method to estimate the VAR(1) model,

X_t = β X_{t-1} + ε_t

where all eigenvalues of β are smaller than one in modulus. The noise vector is assumed to be multivariate normally distributed with mean 0 and covariance Σ.

or SUR model

y_i = X^T β_{i} + ε_{i}

where y_i is N \times 1, β_i is K \times 1 and ε_i is N \times 1; X^T is the design matrix. i = 1,2, ..., m.

Usage

Breg(x,y=NULL,lambda,gamma,alpha=1,type = "var",tol=10^-7,Time=10,r=10^-14,step.size=10^3)

Arguments

x	For type = "var", an N \times K matrix containing observations of the VAR(1) model; For type = "sur", an N \times K design matrix.
y	For type = "var", NULL; For type = "sur", an N \times M response matrix.
lambda	Regularization parameter for β estimation. Must be a nonnegative scalar.
gamma	Regularization parameter for Σ estiamtion. Must be a nonnegative scalar. The penalty is defined as ||P*Σ||_1 where P is a K \times K matrix of all 1 and with 0 on the diagonal to ensure the positive-definiteness.
alpha	Elastic-net mixing parameter as in glmnet, with 0 ≤ α ≤ 1. The coefficient penalty is defined as λ*\{(1-α)/2||β||_2^2+α||β||_1\}. alpha=1 is the lasso penalty, and alpha=0 is the ridge penalty.
type	Model type: "var"(default), "sur".
tol	Convergence threshold for the iterative estimation. The convergence criteria is defined as ||β^{(i)}-β^{(i-1)}||_m ≤ tol ||Σ^{(i)}-Σ^{(i-1)}||_m ≤ tol where 'm' denotes the maximum modulus of all the elements.
Time	Maximum number of iterations.
r	Condition number threshold when check if correlation matrix is singular.
step.size	Parameter used in spcov.

Value

beta	The estimate of coefficients. For type = "var", an K \times K matrix; For type = "sur", a vector of length K*M.
sigma	The estimate of noise variance matrix. For type = "var", an K \times K matrix. For type = "sur", an M \times M matrix.

References

Guanhao Feng and Nicholas G. Polson (2016), Regularizing Bayesian Predictive Regressions. https://arxiv.org/abs/1606.01701

See Also

glmnet,spcov

Examples

## simulating data
beta <- matrix(c(0.9,-0.1,-0.1,0.8),2,2)
x <- t(rep(0,2))
for (i in 1:1000)
  x<-rbind(x,t(beta%*%x[i,])+rnorm(2))
x <- x[-1,]

## estimating the model
Breg(x,lambd=0,gamma=0,alpha=1,tol=10^-3,Time=30)

Jianeng/FinReg documentation built on May 14, 2019, 8:41 a.m.