# interv_covariate

0th

Percentile

##### Describing Intervention Effects for Time Series with Deterministic Covariates

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

Keywords
Intervention detection
##### Usage
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 tau.
##### Details

The intervention effect occuring at time $\tau$ is described by the covariate $$X_t = \delta^{t-\tau} I_{[\tau,\infty)}(t),$$ where $I(t>=\tau)$ is the indicator function which is 0 for $t < \tau$ and 1 for $t >= \tau$. The constant $\delta$ with $0 <= \delta="" <="1$" specifies="" the="" type="" of="" intervention.="" for="" $\delta="0$" intervention="" has="" an="" effect="" only="" at="" time="" its="" occurence,="" $0="" 1$="" decays="" exponentially="" and="" there="" is="" a="" persistent="" after="" occurence.<="" p="">

If tau and delta are vectors, one covariate is generated with tau[1] as $\tau$ and delta[1] as $\delta$, 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.

##### 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.

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