pgam.filter: Estimation of the conditional distributions parameters of the...

In pgam: Poisson-Gamma Additive Models

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 ω 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

Details

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}=ω a_{t-1}

b_{t|t-1}=ω b_{t-1}\exp≤ft(-η_{t}\right)

Once y_{t} is known, the posteriori distribution of μ_{t}|Y_{t} is also gamma with parameters given by

a_{t}=ω a_{t-1}+y_{t}

b_{t}=ω b_{t-1}+\exp≤ft(η_{t}\right)

with t=τ,…,n, where τ 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=τ, where τ 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 [e-mail] and Antonio Ponce de Leon [e-mail]

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

pgam documentation built on Aug. 20, 2022, 1:06 a.m.