PWD (version 1.0)

alphahat_LR_one_Rcpp: Estimates PWD Parameter alpha by Maximum Marginal Predictive Likelihood

Description

This is the main function of the package. It takes as inputs the time series data as response, as well as a predictor matrix, excluding the intercept column, and other settings. It returns as outputs a scalar representing the value of alpha which maximizes the marginal predictive likelihood of the data given the grid of alpha values considered.

Usage

alphahat_LR_one_Rcpp(y, X = FALSE, alpha.grid = seq(0.65, 1, length.out = 150), init = 2, plotting = TRUE)

Arguments

y

T-length time series vector. y[1] represents the beginning of the time eries.

X

[T x p] dimensional matrix of covariates. This should not include the intercept column. If X is FALSE, intercept model is run.

alpha.grid

Grid of alpha values over which to compute the marginal predictive likelihood.

init

integer representing the time point to begin computing marginal predictive likelihoods.

plotting

If TRUE, plot the marginal predictive distribution of alpha.

Value

Return a scalar value representing the value of alpha which maximizes the marginal predictive likelihood of the data over the grid of alpha values considered.

Examples

set.seed(12)
N=80
err = rnorm(N)
X = 1:N
slopes = c(rep(1.5,40),rep(2,N-40))
y = rep(5,N) + slopes*X + err
init=6                
alpha.grid = seq(.75,1,length.out=40)
alphahat=alphahat_LR_one_Rcpp(y=y,X=X,alpha.grid=alpha.grid,init=init,plotting=TRUE)
alpha1 = 1.0
coeffs1 = bhat.func(y,X,alpha1)
alpha2 = alphahat
coeffs2 = bhat.func(y,X,alpha2)
plot(x=X,y=y)
abline(a=coeffs2[1],b=coeffs2[2],lty=2,col="red")
abline(a=coeffs1[1],b=coeffs1[2],lty=2)
legend("right", legend=c("OLS","PWD"), col=c(1,2), lty=c(2,2), lwd=c(1,1))