Description Usage Arguments Value Details References Examples
The function carfima.sim
produces discrete time series data that follow a CARFIMA(p,H,q)
model
given the values for the model parameters and observation times.
1 | carfima.sim(parameter, time, ar.p, ma.q)
|
parameter |
A vector of length p+q+2 for the generative values of the model parameters; p values of α_j's, q values of β_j's, H and σ. |
time |
A vector for the k observation times, either regularly or irregularly spaced. |
ar.p |
A scalar for the order of the AR model. |
ma.q |
A scalar for the order of the MA model. |
The outcome of carfima.sim
is a vector for k simulated data following a CARFIMA(p,H,q)
model given the values for the model parameters and observation times.
This function produces simulated discrete time series data following a CARFIMA(p,H,q)
model given the
values for the model parameters and observation times. It first derives a k-dimensional multivariate
Gaussian distribution whose mean set to a vector of zeroes, where k is the number of observations.
The covariance matrix is then filled with Cov(Y_{t_i}, Y_{t_j}) and its closed-form formula is
specified in Theorem 1(b) and 1(c) of Tsai and Chan (2005).
tsai_maximum_2005carfima
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ##### Irregularly spaced observation time generation.
##### For CRAN testing, time is set to be very short.
length.time <- 10
time.temp <- rexp(length.time, rate = 2)
time <- rep(NA, length.time + 1)
time[1] <- 0
for (i in 2 : (length.time + 1)) {
time[i] <- time[i - 1] + time.temp[i - 1]
}
time <- time[-1]
##### Data genration for CARFIMA(1, H, 0) based on the observation times.
parameter <- c(-0.4, 0.75, 0.2)
# AR parameter alpha = -0.4
# Hurst parameter = 0.75
# process uncertainty sigma = 0.2
y <- carfima.sim(parameter = parameter, time = time, ar.p = 1, ma.q = 0)
|
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