R/generate_data_ou.R

In fChange: Functional Change Point Detection and Analysis

#' Generate Data via Ornstein-Uhlenbeck Process
#'
#' Generate autoregressive process with errors according the Ornstein-Uhlenbeck
#'  process.
#'
#' @param N Numeric for the number of observations.
#' @param v Numeric for resolution of data or a vector specifying the
#'  observation points.
#' @param rho Numeric which indicates the dependence on the previous
#'    curve.
#'
#' @return A dfts object for the generated data.
#' @export
#'
#' @examples
#' generate_ornstein_uhlenbeck(N = 100, v = 20)
generate_ornstein_uhlenbeck <- function(N, v, rho = 0) {
  if (is.null(rho)) {
    rho <- 0
  }
  if (length(v) == 1) {
    v <- seq(0, 1, length.out = v)
  }
  r <- length(v)

  # Covariance structure (OU process Cov)
  comat <- matrix(NA, r, r)
  for (i in 1:r) {
    comat[i, ] <- exp(-abs(v[i] - v) / 2)
  }

  fiid <- MASS::mvrnorm(
    n = N,
    mu = rep(0, r),
    Sigma = comat,
    empirical = TRUE
  )

  data <- data.frame(matrix(0, ncol = nrow(fiid), nrow = ncol(fiid)))
  data[, 1] <- fiid[1, ]
  for (i in 2:ncol(data)) {
    data[, i] <- rho * data[, i - 1] + fiid[i, ]
  }

  dfts(data)
}