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

Campos, E. L., De Leon, A. C. M. P., Fernandes, C. A. C. (2003) Modelo Poisson-Gama para Séries Temporais de Dados de Contagem - Teoria e Aplicações. 10a ESTE - Escola de Séries Temporais e Econometria

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

See Also

pgam, pgam.filter, pgam.fit


[Package pgam version 0.4.5 Index]