Simulate MARMA(p,q) Processes
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
|
theta |
A vector of non-negative parameters, of length
|
init |
A vector of non-negative starting values, of
length |
n.start |
A non-negative value denoting the length of the
burn-in period. If |
rand.gen |
A simulation function to generate the innovations. |
... |
Additional arguments for |
A max autoregressive moving average process {X_k}, denoted by MARMA(p,q), is defined in Davis and Resnick (1989) as satisfying
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
\code{phi} = (phi_1, …, phi_p)
and
\code{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.
Davis, R. A. and Resnick, S. I. (1989) Basic properties and prediction of max-arma processes. Adv. Appl. Prob., 21, 781–803.
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))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.