tsglm.izip: Fit an integered-valued GARCH time series iZIP Model

In thomas-fung/izipr: Interpretable Zero-Inflated Poisson Models in R

Description

The function tsglm.izip is used to fit an iZIP integer-valued INGARCH model with identity link. The estimation is done by qausi-likelihood approach based on the Poisson likelihood function.

Usage

tsglm.izip(
  formula,
  past_mean_lags = 1,
  past_obs_lags = 1,
  data,
  ref.lambda = NULL,
  ...
)

Arguments

formula	an object of class 'formula': a symbolic description of the response and exogenous regressors.
past_mean_lags	numeric vector: integer vector giving the previous conditional means to be regressed on. If omitted, or of length zero, there will be no regression on previous observations.
past_obs_lags	numeric vector: integer vector giving the previous observations to be regressed on (autoregression). If omitted, or of length zero, there will be no regression on previous conditional means.
data	an optional data frame containing the variables in the model
ref.lambda	the rate of a Poisson distribution that baseline zero-inflated odds based on.
...	additional arguments to be passed to the lower level fitting function tsglm. See ?tscount::tsglm for more details.

Details

Fit an integered-valued GARCH time series iZIP Model.

The model is

Y_i ~ ZIP_{ν}(μ_i | λ = λ_{ref}),

where

E(Y_i) = μ_i = x_i^T β + α_1μ_{t-1} + … + α_sμ_{t-s} + β_1Y_{t-1} + … + β_q Y_{t-q},

x_i are some covariates.

ν ≥ 0 is the baseline zero-inflated odds relative to a Poisson with rate λ_{ref}.

Value

A fitted model object of class tsizip similar to one obtained from tsglm.

The function summary (i.e., summary.tsizip) can be used to obtain and print a summary of the results.

The functions plot (i.e., plot.tsizip) and autoplot can be used to produce a range of diagnostic plots.

The generic assessor functions coef (i.e., coef.tsizip), logLik (i.e., logLik.tsizip) fitted (i.e., fitted.tsizip), nobs (i.e., nobs.tsizip), AIC (i.e., AIC.tsizip) and residuals (i.e., residuals.tsizip) can be used to extract various useful features of the value returned by tsglm.izip.

An object class 'tsizip' is a list containing at least the following components:

coefficients	a named vector of coefficients
stderr	robust standard errors (using the sandwich estimators)
residuals	the response residuals (i.e., observed-fitted)
fitted_values	the fitted mean values
y	the y vector used.
X	the model matrix for mean
model	the model frame for regression
call	the matched call
formula	the formula supplied for regression
terms	the terms object used for regression
data	the data argument

References

Huang, A. and Fung, T. (2020). Zero-inflated Poisson exponential families, with applications to time-series modelling of counts.

Examples

data(arson)
M_arson <- tsglm.izip(arson ~ 1, past_mean_lags = 1, past_obs_lags = c(1, 2))
summary(M_arson)
plot(M_arson) # or autoplot(M_arson)

thomas-fung/izipr documentation built on Dec. 23, 2021, 9:57 a.m.