Functions to calculate the analytical mean, variance and autocorrelation / partial autocorrelation / autocovariance function of an integervalued generalised autoregressive conditional heteroscedasticity (INGARCH) process.
1 2 3 4  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, ...)

intercept 
numeric positive value for the intercept β[0]. 
past_obs 
numeric nonnegative vector containing the coefficients β[1], …, β[p] for regression on previous observations (see Details). 
past_mean 
numeric nonnegative 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 
plot 
logical. If 
... 
additional arguments to be passed to function 
The INGARCH model of order p and q used here follows the definition
Z[t]F[t1] ~ Poi(κ[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 κ[t] is given by
κ[t] = β[0] + β[1] Z[t1] + … + β[p] Z[tp] + α[1] κ[t1] + … + α[q] κ[tq].
The function ingarch.acf
depends on the function tacvfARMA
from package ltsa
, which needs to be installed.
Tobias Liboschik
Ferland, R., Latour, A. and Oraichi, D. (2006) Integervalued GARCH process. Journal of Time Series Analysis 27(6), 923–942, http://dx.doi.org/10.1111/j.14679892.2006.00496.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.
1 2 3 4 5  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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