pgam.fit: One-step ahead prediction and variance

Description

Estimate one-step ahead expectation and variance of $y_{t}$ conditional on observed time series until the instant $t-1$.

Usage

pgam.fit(w, y, eta, partial.resid)

Arguments

estimate of discount factor $\omega$ of a Poisson-Gamma model

observed time series which is the response variable of the model

eta

semiparametric predictor

partial.resid

type of partial residuals.

Value

yhatvector of one-step ahead prediction
residvector partial residuals

Details

Partial residuals for semiparametric estimation is extracted. Those are regarded to the parametric partition fit of the model. Available types are raw, pearson and deviance. The type raw is prefered. Properties of other form of residuals not fully tested. Must be careful on choosing it. See details in predict.pgam and residuals.pgam.

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

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

Green, P. J., Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: a roughness penalty approach. Chapman and Hall, London