pcme.entropy {pcme} | R Documentation |
Compute the entropy of a periodically correlated time series model and its derivatives with respect to unknown autocovariances.
sigma2.to.ent(sigma2) sigma2.to.entgrad(sigma2, gradsigma2) sigma2.to.enthess(sigma2, gradsigma2, grad2sigma2) mynorm(x)
sigma2 |
vector of forward prediction variances. |
gradsigma2 |
gradient of forward prediction variances. |
grad2sigma2 |
Hessian matrix of forward prediction variances. |
x |
a numeric vector of prediction variances. |
for sigma2.to.ent
the entropy, a numeric scalar.
for sigma2.to.entgrad
the gradient of the entropy, a numeric vector.
for sigma2.to.enthess
the Hessian of the entropy, a matrix.
Sophie Lambert-Lacroix
Boshnakov, Georgi and Lambert-Lacroix, Sophie (2009?) Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients. J. Time Series Anal. (to appear)
sigma2.to.ent(c(1,0.50,0.8)) # -0.3054302 sum(log(c(1,0.50,0.8)))/3 # same ##ex From myhessian.r R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3) Tau <- matrix(c(1,1,1,0,1,0,1,0,2,1,2,2),nrow=3) R[,1]<-R[,1]+1 LD(R,Tau) res <- LDhessian(R,Tau) sigma2.to.ent(res$sigma2f) sigma2.to.entgrad(res$sigma2f,res$gradsigma2f) H <- sigma2.to.enthess(res$sigma2f,res$gradsigma2f,res$grad2sigma2f) det(-H)