dgp.far: FAR(p) Data Generator

In FTSgof: White Noise and Goodness-of-Fit Tests for Functional Time Series

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)

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.

Value

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

Examples

# 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)

FTSgof documentation built on Oct. 4, 2024, 1:06 a.m.