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.

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)
# }