rsfar function

Simulation of a Seasonal Functional Autoregressive SFAR(1) process.

Simulation of a Seasonal Functional Autoregressive SFAR(1) process.

Simulation of a SFAR(1) process on a Hilbert space of L2[0,1].

rsfar(phi, seasonal, Z)

Arguments

  • phi: a kernel function corresponding to the seasonal autoregressive operator.
  • seasonal: a positive integer variable specifying the seasonal period.
  • Z: the functional noise object of the class 'fd'.

Returns

A sample of functional time series from a SFAR(1) model of the class fd.

Examples

# Set up Brownian motion noise process N <- 300 # the length of the series n <- 200 # the sample rate that each function will be sampled u <- seq(0, 1, length.out = n) # argvalues of the functions d <- 15 # the number of basis functions basis <- create.fourier.basis(c(0, 1), d) # the basis system sigma <- 0.05 # the stdev of noise norm Z0 <- matrix(rnorm(N * n, 0, sigma), nr = n, nc = N) Z0[, 1] <- 0 Z_mat <- apply(Z0, 2, cumsum) # N standard Brownian motion Z <- smooth.basis(u, Z_mat, basis)$fd # Compute the standardized constant of a kernel function with respect to a given HS norm. gamma0 <- function(norm, kr) { f <- function(x) { g <- function(y) { kr(x, y)^2 } return(integrate(g, 0, 1)$value) } f <- Vectorize(f) A <- integrate(f, 0, 1)$value return(norm / A) } # Definition of parabolic integral kernel: norm <- 0.99 kr <- function(x, y) { 2 - (2 * x - 1)^2 - (2 * y - 1)^2 } c0 <- gamma0(norm, kr) phi <- function(x, y) { c0 * kr(x, y) } # Simulating a path from an SFAR(1) process s <- 5 # the period number X <- rsfar(phi, s, Z) plot(X)