pgam.filter {pgam} | R Documentation |
Estimation of the conditional distributions parameters of the level
Description
The priori and posteriori conditional distributions of the level is gamma and their parameters are estimated through this recursive filter. See Details for a thorough description.
Usage
pgam.filter(w, y, eta)
Arguments
w |
running estimate of discount factor |
y |
|
eta |
full linear or semiparametric predictor. Linear predictor is a trivial case of semiparameric model |
Details
Consider Y_{t-1}
a vector of observed values of a Poisson process untill the instant t-1
. Conditional on that, \mu_{t}
has gamma distribution with parameters given by
a_{t|t-1}=\omega a_{t-1}
b_{t|t-1}=\omega b_{t-1}\exp\left(-\eta_{t}\right)
Once y_{t}
is known, the posteriori distribution of \mu_{t}|Y_{t}
is also gamma with parameters given by
a_{t}=\omega a_{t-1}+y_{t}
b_{t}=\omega b_{t-1}+\exp\left(\eta_{t}\right)
with t=\tau,\ldots,n
, where \tau
is the index of the first non-zero observation of y
.
Diffuse initialization of the filter is applied by setting a_{0}=0
and b_{0}=0
. A proper distribution of \mu_{t}
is obtained at t=\tau
, where \tau
is the fisrt non-zero observation of the time series.
Value
A list containing the time varying parmeters of the priori and posteriori conditional distribution is returned.
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.
See Also
pgam
, pgam.likelihood
, pgam.fit
, predict.pgam