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 |
env |
the caller environment for log-likelihood value to be stored |
Details
Log-likelihood function of hyperparameters \omega
and \beta
is given by
\log L\left(\omega,\beta\right)=\sum_{t=\tau+1}^{n}{\log \Gamma\left(a_{t|t-1}+y_{t}\right)-\log y_{t}!-\log \Gamma\left(a_{t|t-1}\right)+a_{t|t-1}\log b_{t|t-1}-\left(a_{t|t-1}+y_{t}\right)\log \left(1+b_{t|t-1}\right)}
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) Semiparametric Poisson-Gamma models: a roughness penalty approach. MSc Dissertation. Rio de Janeiro, PUC-Rio, Department of Electrical Engineering.