# Describing Intervention Effects for Time Series with Deterministic Covariates

### Description

Generates covariates describing certain types of intervention effects according to the definition by Fokianos and Fried (2010).

### Usage

1 | ```
interv_covariate(n, tau, delta)
``` |

### Arguments

`n` |
integer value giving the number of observations the covariates should have. |

`tau` |
integer vector giving the times where intervention effects occur. |

`delta` |
numeric vector with constants specifying the type of intervention (see Details). Must be of the same length as |

### Details

The intervention effect occuring at time *τ* is described by the covariate

*X_t = δ^(t-τ) I(t>=τ),*

where *I(t>=τ)* is the indicator function which is 0 for *t < τ* and 1 for *t >= τ*. The constant *δ* with *0 <= δ <= 1* specifies the type of intervention. For *δ = 0* the intervention has an effect only at the time of its occurence, for *0 < δ < 1* the effect decays exponentially and for *δ = 1* there is a persistent effect of the intervention after its occurence.

If `tau`

and `delta`

are vectors, one covariate is generated with `tau[1]`

as *τ* and `delta[1]`

as *δ*, another covariate for the second elements and so on.

### Value

A matrix with `n`

rows and `length(tau)`

columns. The generated covariates describing the interventions are the columns of the matrix.

### Author(s)

Tobias Liboschik

### References

Fokianos, K. and Fried, R. (2010) Interventions in INGARCH processes. *Journal of Time Series Analysis* **31(3)**, 210–225, http://dx.doi.org/10.1111/j.1467-9892.2010.00657.x.

Fokianos, K., and Fried, R. (2012) Interventions in log-linear Poisson autoregression. *Statistical Modelling* **12(4)**, 299–322. http://dx.doi.org/10.1177/1471082X1201200401.

Liboschik, T., Kerschke, P., Fokianos, K. and Fried, R. (2014) Modelling interventions in INGARCH processes. *International Journal of Computer Mathematics* (published online), http://dx.doi.org/10.1080/00207160.2014.949250.

### See Also

`tsglm`

for fitting a GLM for time series of counts.
`interv_test`

, `interv_detect`

and `interv_multiple`

for tests and detection procedures for intervention effects.

### Examples

1 | ```
interv_covariate(n=140, tau=c(84,100), delta=c(1,0))
``` |