# ingarch.analytical: Analytical Mean, Variance and Autocorrelation of an INGARCH... In tscount: Analysis of Count Time Series

## 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

 ```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, ...) ```

## 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.

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

 ```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) ```

### Example output

```[1] 0.4285714
[1] 0.4397032
```

tscount documentation built on Nov. 25, 2017, 1:04 a.m.