# Compute the Autoregressive Representation of a SARIMA Model Invert (invertible) SARIMA(p, d, q, P, D, Q) models to ar representation. ```r arrep(notation = "arima", phi = c(rep(0, 10)), d = 0, theta = c(rep(0, 10)), Phi = c(rep(0, 10)), D = 0, Theta = c(rep(0, 10)), frequency = 1) ``` ## Arguments - `notation`: "arima" for notation of the type used by the function arima(stats), "dse1" for type notation used by the package dse1. - `phi`: p vector of autoregressive coefficient. - `d`: difference operator, implemented: d element of (0,1,2). - `theta`: q vector of moving average coefficients. - `Phi`: P vector of seasonal autoregressive coefficients. - `D`: Seasonal difference operator, implemented: D element of (0,1,2). - `Theta`: Q vector of seasonal moving average coefficients. - `frequency`: The frequency of the seasonality (e.g. frequency = 12 for monthly series with annual periodicity). ## Details For input, positive values of phi, theta, Phi and Theta indicate positive dependence. Implemented for p,q,P,Q element of c(0,1,2,3,4,5,6,7,8,9,10). The ar representation is truncated at coefficients less than 1.0e-10. Values of theta, Theta near non invertibility (-1 or 1) will not be practical and will cause near infinite lags, especially for Theta and large frequency. ## Returns A vector containing a truncated autoregressive representation of a SARIMA model. This can be used as input for the function gar.sim. ## References Briet OJT, Amerasinghe PH, Vounatsou P: Generalized seasonal autoregressive integrated moving average models for count data with application to malaria time series with low case numbers. PLoS ONE, 2013, 8(6): e65761. doi:10.1371/journal.pone.0065761 [https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0065761](https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0065761) If you use the gsarima package, please cite the above reference. ## Author(s) Olivier Briet o.briet@gmail.com ## See Also 'garsim'. ## Examples ```r phi<-c(0.5, 0.3, 0.1) theta<-c(0.6, 0.2, 0.2) ar<-arrep(phi=phi, theta=theta, frequency=12) check<-(acf2AR(ARMAacf(ar=phi, ma=theta, lag.max = 100, pacf = FALSE))[100,1:length(ar)]) as.data.frame(cbind(ar,check)) phi<-c(0.2,0.5) theta<-c(0.4) Phi<-c(0.6) Theta<-c(0.3) d<-2 D<-1 frequency<-12 ar<-arrep(phi=phi, theta=theta, Phi=Phi, Theta=Theta, frequency= frequency, d=d, D=D) N<-500 intercept<-10 data.sim <- garsim(n=(N+length(ar)),phi=ar, X=matrix(rep(intercept,(N+ length(ar)))), beta=1, sd=1) y<-data.sim[1+length(ar): (N+length(ar))] tsy<-ts(y, freq= frequency) plot(tsy) arima(tsy, order=c(2,2,1), seasonal=list(order=c(1,1,1))) ```

arrep function