tscount (version 1.4.3)

ingarch.analytical: Analytical Mean, Variance and Autocorrelation of an INGARCH Process

Description

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 \(\beta_0\).

past_obs

numeric non-negative vector containing the coefficients \(\beta_1,\ldots, \beta_p\) for regression on previous observations (see Details).

past_mean

numeric non-negative 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 $$Z_{t}|{\cal{F}}_{t-1} \sim \mathrm{Poi}(\kappa_{t}),$$ where \({\cal{F}}_{t-1}\) is the history of the process up to time \(t-1\) and \(\mathrm{Poi}\) 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.

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

Run this code
# NOT RUN {
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)
# }

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