ingarch.analytical
Analytical Mean, Variance and Autocorrelation of an INGARCH Process
Functions to calculate the analytical mean, variance and autocorrelation / partial autocorrelation / autocovariance function of an integervalued generalised autoregressive conditional heteroscedasticity (INGARCH) process.
Usage
ingarch.mean(intercept, past_obs=NULL, past_mean=NULL)
ingarch.var(intercept, past_obs=NULL, past_mean=NULL)
ingarch.acf(intercept, past_obs=NULL, past_mean=NULL, lag.max=10, type=c("acf", "pacf", "acvf"), plot=TRUE, ...)
Arguments
 intercept
 numeric positive value for the intercept $\beta[0]$.
 past_obs
 numeric nonnegative vector containing the coefficients $\beta[1], \ldots, \beta[p]$ for regression on previous observations (see Details).
 past_mean
 numeric nonnegative vector containing the coefficients $\alpha[1], \ldots, \alpha[q]$ for regression on previous conditional means (see Details).
 lag.max
 integer value indicating how many lags of the (partial) autocorrelation / autocovariance function should be calculated.
 type

character. If
type="acf"
(the default) the autocorrelation function is calculated,"pacf"
gives the partial autocorrelation function and"acvf"
the autocovariance function.  plot

logical. If
plot=TRUE
(the default) the values are plotted and returned invisible.  ...

additional arguments to be passed to function
plot
.
Details
The INGARCH model of order $p$ and $q$ used here follows the definition
$$Z_{t}{\cal{F}}_{t1} \sim \mathrm{Poi}(\kappa_{t}),$$
where $F[t1]$ is the history of the process up to time $t1$ and $Poi$ is the Poisson distribution parametrised by its mean (cf. Ferland et al., 2006).
The conditional mean $\kappa[t]$ is given by
$$\kappa_t = \beta_0 + \beta_1 Z_{t1} + \ldots + \beta_p Z_{tp}
+ \alpha_1 \kappa_{t1} + \ldots + \alpha_q \kappa_{tq}.$$
The function ingarch.acf
depends on the function tacvfARMA
from package ltsa
, which needs to be installed.
References
Ferland, R., Latour, A. and Oraichi, D. (2006) Integervalued GARCH process. Journal of Time Series Analysis 27(6), 923942, http://dx.doi.org/10.1111/j.14679892.2006.00496.x.
See Also
tsglm
for fitting a more genereal GLM for time series of counts of which this INGARCH model is a special case. tsglm.sim
for simulation from such a model.
Examples
ingarch.mean(0.3, c(0.1,0.1), 0.1)
## Not run:
# ingarch.var(0.3, c(0.1,0.1), 0.1)
# ingarch.acf(0.3, c(0.1,0.1,0.1), 0.1, type="acf", lag.max=15)## End(Not run)