Solved – How to generate the time series from a given model

We consider a sparse autoregressive time series of length 1000 obeying the model


with nonzero coefficients at lags 1,3,5,10 and 15,where the innovations Z(t) are i.i.d. Gaussians with mean zero and standard deviation 0.1.

The question is how to simulate 1000 time series from the model with R or SAS?

In R, fill a vector with Gaussian white noise of zero mean and sd 0.1, then use the filter function. Notice that since the first 15 observations are white noise (and thence not generated by your model), you have to discard a section of your generated observations (say 10 times the maximum lag).

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