simulate_iid_brownian_bridge {fdaACF}

Simulate a FTS from a brownian bridge process

Description

Generate a functional time series from a Brownian Bridge process. If W(t) is a Wiener process, the Brownian Bridge is defined as W(t) - tW(1). Each functional observation is discretized in the points indicated in v. The series obtained is i.i.d. and does not exhibit any kind of serial correlation.

Usage

simulate_iid_brownian_bridge(N, v = seq(from = 0, to = 1, length.out =
  100), sig = 1)

Arguments

N

The number of observations of the simulated data.

v

Discretization points of the curves, by default seq(from = 0, to = 1, length.out = 100).

sig

Standard deviation of the Brownian Motion process, by default 1.

Value

Return the simulated functional time series as a matrix.

Examples

N <- 100
v <- seq(from = 0, to = 1, length.out = 20)
sig <- 2
bbridge <- simulate_iid_brownian_bridge(N, v, sig)
matplot(v,t(bbridge), type = "l", xlab = "v", ylab = "Value")