[R] Model Based Bootstrap

[Andreas Klein]

Hello.

Has anyone any idea how a function would look like of a model based bootstrap, when the underlying time series follows an ARIMA(1,1,1)-process?
A pure AR-process is no problem, but what is, if the time series need to be differentiated of order one or above and the additional MA-part?

Sample code for a series, which follows a pure AR-process:

#Series y of 192 observations, which follows an AR(1)-process
#Fit of an AR(1)-Model to y

ar.coef     <- ar(y)$ar
ar.resid    <- ar(y)$resid

#Sampling for mean

y_sample    <- numeric(192)
y_sample[1] <- y[1]
mean_y      <- numeric(10000)

for (i in 1:10000)

{

 for (j in 1:191)

 {

  idx           <- sample(2:192,1,replace=TRUE)
  y_sample[j+1] <- y_sample[j]*ar.coef+ar.resid[idx]

 }

 mean_y[i] <- mean(y_sample)
 
}


What would the function look like if y follows an ARIMA(1,1,1)-process for example or in general if y is a time series, which need to be differentiated and is best modeled with a mixture of AR and MA?

I hope you can help me.

Sincerely
Andreas.


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