# ingarch.analytical

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Percentile

##### Analytical Mean, Variance and Autocorrelation of an INGARCH Process

Functions to calculate the analytical mean, variance and autocorrelation / partial autocorrelation / autocovariance function of an integer-valued 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 $\beta$.
past_obs
numeric non-negative vector containing the coefficients $\beta, \ldots, \beta[p]$ for regression on previous observations (see Details).
past_mean
numeric non-negative vector containing the coefficients $\alpha, \ldots, \alpha[q]$ 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 $$Z_{t}|{\cal{F}}_{t-1} \sim \mathrm{Poi}(\kappa_{t}),$$ where $F[t-1]$ is the history of the process up to time $t-1$ and $Poi$ is the Poisson distribution parametrised by its mean (cf. Ferland et al., 2006). The conditional mean $\kappa[t]$ is given by $$\kappa_t = \beta_0 + \beta_1 Z_{t-1} + \ldots + \beta_p Z_{t-p} + \alpha_1 \kappa_{t-1} + \ldots + \alpha_q \kappa_{t-q}.$$ 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) Integer-valued GARCH process. Journal of Time Series Analysis 27(6), 923--942, http://dx.doi.org/10.1111/j.1467-9892.2006.00496.x.

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.

##### Aliases
• ingarch.analytical
• ingarch.mean
• ingarch.acf
• ingarch.var
##### 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)

Documentation reproduced from package tscount, version 1.3.0, License: GPL-2 | GPL-3

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