Simulate GLP given innovations
Simulates a General Linear Time Series that can have nonGaussian innovations.
It uses the FFT so it is O(N log(N)) flops where N=length(a) and N is assumed
to be a power of 2.
The R function convolve is used which implements the FFT.
SimGLP(psi, a)
psi |
vector, length Q, of MA coefficients starting with 1. |
a |
vector, length Q+n, of innovations, where n is the length of time series to be generated. |
z_t = ∑_{k=0}^Q psi_k a_{t-k}
where t=1,…,n and the innovations $a_t, t=1-Q, ..., 0, 1, ..., n$ are given in the input vector a.
Since convolve uses the FFT this is faster than direct computation.
vector of length n, where n=length(a)-length(psi)
A.I. McLeod
#Simulate an AR(1) process with parameter phi=0.8 of length n=100 with # innovations from a t-distribution with 5 df and plot it. # phi<-0.8 psi<-phi^(0:127) n<-100 Q<-length(psi)-1 a<-rt(n+Q,5) z<-SimGLP(psi,a) z<-ts(z) plot(z)
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