pgam.likelihood {pgam}R Documentation

Likelihood function to be maximized

Description

This is the log-likelihood function that is passed to optim for likelihood maximization.

Usage

pgam.likelihood(par, y, x, offset, fperiod, env = parent.frame())

Arguments

par vector of parameters to be optimized
y observed time series which is the response variable of the model
x observed explanatory variables for parametric fit
offset model offset. Just like in GLM
fperiod vector of seasonal factors to be passed to pgam.par2psi
env the caller environment for log-likelihood value to be stored

Details

Log-likelihood function of hyperparameters omega and β is given by

log L(omega,β)=sum_{t=tau+1}^{n}{log Γ(a_{t|t-1}+y_{t})-log y_{t}!-
log Γ(a_{t|t-1})+a_{t|t-1}log b_{t|t-1}-(a_{t|t-1}+y_{t})log (1+b_{t|t-1})}

where a_{t|t-1} and b_{t|t-1} are estimated as it is shown in pgam.filter.

Value

List containing log-likelihood value, optimum linear predictor and the gamma parameters vectors.

Note

This function is not intended to be called directly.

Author(s)

Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br

References

Harvey, A. C., Fernandes, C. (1989) Time series models for count data or qualitative observations. Journal of Business and Economic Statistics, 7(4):407–417

Harvey, A. C. (1990) Forecasting, structural time series models and the Kalman Filter. Cambridge, New York

Junger, W. L. (2004) Modelo Poisson-Gama Semi-Parametrico: Uma Abordagem de Penalizacao por Rugosidade. MSc Thesis. Rio de Janeiro, PUC-Rio, Departamento de Engenharia Eletrica

See Also

pgam, pgam.filter, pgam.fit


[Package pgam version 0.4.8 Index]