marma {evd} | R Documentation |
Simulation of MARMA(p,q) processes.
marma(n, p = 0, q = 0, psi, theta, init = rep(0, p), n.start = p, rand.gen = rfrechet, ...) mar(n, p = 1, psi, init = rep(0, p), n.start = p, rand.gen = rfrechet, ...) mma(n, q = 1, theta, rand.gen = rfrechet, ...)
n |
The number of observations. |
p |
The AR order of the MARMA process. |
q |
The MA order of the MARMA process. |
psi |
A vector of non-negative parameters, of length
p . Can be omitted if p is zero. |
theta |
A vector of non-negative parameters, of length
q . Can be omitted if q is zero. |
init |
A vector of non-negative starting values, of
length p . |
n.start |
A non-negative value denoting the length of the
burn-in period. If n.start is less than p , then
p minus n.start starting values will be included
in the output series. |
rand.gen |
A simulation function to generate the innovations. |
... |
Additional arguments for rand.gen . Most
usefully, the scale and shape parameters of the innovations
generated by rfrechet can be specified by scale
and shape respectively. |
A max autoregressive moving average process {X_k}, denoted by MARMA(p,q), satisfies
X_k = max[phi_1 X_{k-1}, ..., phi_p X_{k-p}, epsilon_k, theta_1 epsilon_{k-1}, ..., theta_q epsilon_{k-q}]
where phi
= (phi_1, ..., phi_p)
and theta
= (theta_1, ..., theta_q)
are non-negative vectors of parameters, and where
{epsilon_k} is a series of iid
random variables with a common distribution defined by
rand.gen
.
The functions mar
and mma
generate MAR(p) and
MMA(q) processes respectively.
A MAR(p) process {X_k} is equivalent to a
MARMA(p, 0) process, so that
X_k = max[phi_1 X_{k-1}, ..., phi_p X_{k-p}, epsilon_k].
A MMA(q) process {X_k} is equivalent to a MARMA(0, q) process, so that
X_k = max[epsilon_k, theta_1 epsilon_{k-1}, ..., theta_q epsilon_{k-q}].
A numeric vector of length n
.
marma(100, p = 1, q = 1, psi = 0.75, theta = 0.65) mar(100, psi = 0.85, n.start = 20) mma(100, q = 2, theta = c(0.75, 0.8))