pgam.filter {pgam} | R Documentation |
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.
pgam.filter(w, y, eta)
w |
running estimate of discount factor omega of a Poisson-Gamma model |
y |
n length vector of the time series observations |
eta |
full linear or semiparametric predictor. Linear predictor is a trivial case of semiparameric model |
Consider Y_{t-1} a vector of observed values of a Poisson process untill the instant t-1. Conditional on that, μ_{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(-eta_{t})
Once y_{t} is known, the posteriori distribution of μ_{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(eta_{t})
with t=tau,...,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 μ_{t} is obtained at t=tau, where tau is the fisrt non-zero observation of the time series.
A list containing the time varying parmeters of the priori and posteriori conditional distribution is returned.
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-Paramérico: Uma Abordagem de Penalização por Rugosidade. MSc Thesis. Rio de Janeiro, PUC-Rio, Departamento de Engenharia Elétrica
pgam
, pgam.likelihood
, pgam.fit
, predict.pgam