R lasso

library(HDeconometrics)
data("BRinf")
data=embed(BRinf,2)
y=data[,1]; x=data[,-c(1:ncol(BRinf))]

## == Break the data into in-sample and out-of-sample
y.in=y[1:100]; y.out=y[-c(1:100)]
x.in=x[1:100,]; x.out=x[-c(1:100),]

## == LASSO == ##
lasso=ic.glmnet(x.in,y.in,crit = "bic")
plot(lasso$glmnet,"lambda",ylim=c(-2,2))


plot(lasso)

# # # Now we can calculate the forecast:

## == Forecasting == ##
pred.lasso=predict(lasso,newdata=x.out)
plot(y.out, type="l")
lines(pred.lasso, col=2)

## = adaLASSO = ##
tau=1
first.step.coef=coef(lasso)[-1]
penalty.factor=abs(first.step.coef+1/sqrt(nrow(x)))^(-tau)
adalasso=ic.glmnet(x.in,y.in,crit="bic",penalty.factor=penalty.factor)
pred.adalasso=predict(adalasso,newdata=x.out)

plot(y.out, type="l")
lines(pred.lasso, col=2)
lines(pred.adalasso, col=4)

## = comparing the errors = ##
c(LASSO=sqrt(mean((y.out-pred.lasso)^2)), 
  adaLASSO=sqrt(mean((y.out-pred.adalasso)^2)))