FTSgof (version 1.0.0)

dgp.far: FAR(p) Data Generator

Description

It generates functional data that follows a functional autoregressive process of order \(p\), denoted as FAR(p). The generated data consists of curves evaluated at discrete grid points.

Usage

dgp.far(J, N, S = 0.5, p = 1, kernel = "Gaussian", burn_in = 50)

Value

A \(J \times N\) matrix where each column contains a curve evaluated at \(J\) grid points, generated from the FAR(p) model.

Arguments

J

The number of grid points for each curve observation.

N

The sample size, representing the number of curves to be generated.

S

The serial dependence factor for the kernel used in the FAR(p) process. Default is 0.5.

p

The order of the autoregressive process. Default is 1.

kernel

The type of kernel function \(\psi\) used for the autoregressive process. Can be "Gaussian" or "Wiener". Default is "Gaussian".

burn_in

The number of initial points discarded to eliminate transient effects. Default is 50.

Details

The functional autoregressive model of order \(p\) is given by: $$X_i(t) -\mu(t) = \sum_{j=1}^{p} \Psi(X_{i-j}-\mu)(t) + \epsilon_i(t),$$ where \(\Psi(X)(t) = \int \psi(t,s)X(s) dt\) is the kernel operator, and \(\epsilon_i(t)\) are i.i.d. errors generated from a standard Brownian motion process. The mean function \(\mu\) is assumed to be zero in the generating process.

Examples

# \donttest{
# Generate discrete evaluations of 200 curves, each observed at 50 grid points.
yd_far = dgp.far(J = 50, N = 200, S = 0.7, p = 2, kernel = "Gaussian", burn_in = 50)
# }