pgam.likelihood {pgam} | R Documentation |
This is the log-likelihood function that is passed to optim
for likelihood maximization.
pgam.likelihood(par, y, x, offset, fperiod, env = parent.frame())
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 |
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
.
List containing log-likelihood value, optimum linear predictor and the gamma parameters vectors.
This function is not intended to be called directly.
Washington Leite Junger wjunger@ims.uerj.br and Antonio Ponce de Leon ponce@ims.uerj.br
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