ltsa (version 1.4.6.1)

SimGLP: Simulate GLP given innovations

Description

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.

Usage

SimGLP(psi, a)

Value

vector of length n, where n=length(a)-length(psi)

Arguments

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.

Author

A.I. McLeod

Details

$$ z_t = \sum_{k=0}^Q psi_k a_{t-k} $$ where \(t=1,\ldots,n\) 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.

See Also

convolve, arima.sim

Examples

#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)