Analytical Mean, Variance and Autocorrelation of an INGARCH Process

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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

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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 β[0].

past_obs

numeric non-negative vector containing the coefficients β[1], …, β[p] for regression on previous observations (see Details).

past_mean

numeric non-negative vector containing the coefficients α[1], …, α[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]|F[t-1] ~ Poi(κ[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 κ[t] is given by

κ[t] = β[0] + β[1] Z[t-1] + … + β[p] Z[t-p] + α[1] κ[t-1] + … + α[q] κ[t-q].

The function ingarch.acf depends on the function tacvfARMA from package ltsa, which needs to be installed.

Author(s)

Tobias Liboschik

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

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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)

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