ts-models-tvARMA {forecastSNSTS} | R Documentation |
Simulation of an tvARMA(p,q) time series.
Description
Returns a simulated time series Y_{1,T}, ..., Y_{T,T}
that fulfills
the following equation:
Y_{t,T} = \sum_{j=1}^p a_j(t/T) Y_{t-j,T} + \sigma(t/T) \varepsilon_{t} + \sum_{k=1}^q \sigma((t-k)/T) b_k(t/T) \varepsilon_{t-k},
where a_1, \ldots, a_p, b_0, b_1, \ldots, b_q
are real-valued functions on [0,1]
,
\sigma
is a positive function on [0,1]
and \varepsilon_t
is white noise.
Usage
tvARMA(T = 128, a = list(), b = list(), sigma = function(u) {
return(1) }, innov = function(n) { rnorm(n, 0, 1) })
Arguments
T |
length of the time series to be returned |
a |
list of p real-valued functions defined on |
b |
list of q real-valued functions defined on |
sigma |
function |
innov |
a function with one argument |
Value
Returns a tvARMA(p,q) time series with specified parameters.
Examples
## Taken from Section 6 in Dahlhaus (1997, AoS)
a1 <- function(u) {1.8 * cos(1.5 - cos(4 * pi * u))}
a2 <- function(u) {-0.81}
plot(tvARMA(128, a = list(a1, a2), b = list()), type = "l")
[Package forecastSNSTS version 1.3-0 Index]