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Simulate a FARFIMA(p, d, q) process

sim_farfima.Rd

Simulates n curves from a FARFIMA(p, d, q) model on no_grid equally spaced points of [0, 1]. The innovations are Brownian motion curves. They are fractionally integrated with memory parameter d, passed through the MA operators and then through the AR recursion. The first 100 curves are dropped as burn-in.

Usage

sim_farfima(
  n = 500,
  d = 0.1,
  p = 1,
  q = 0,
  no_grid = 101,
  seed = NULL,
  ar_strength = 0.6,
  ma_strength = 0.6,
  lag_strength = c("equal", "decay")
)

Arguments

n

Number of curves.

d

Memory parameter.

p, q

AR and MA orders, not both zero.

no_grid

Number of grid points.

seed

Optional seed.

ar_strength, ma_strength

Operator strengths \(\psi\) and \(\nu\).

lag_strength

"equal" splits the strength equally across lags, and "decay" lets it decay geometrically.

Value

A matrix of curves, no_grid by n. The innovations are kept in attr(, "innovations").

Details

The AR kernel is \(\exp\{(u^2 + v^2)/2\}\) and the MA kernel is \(\min(u, v)\). Each is scaled to operator norm one and multiplied by ar_strength or ma_strength.

See also

split_curves(), farfima()

Examples

sim = sim_farfima(n = 200, d = 0.2, p = 1, q = 1, seed = 1)
dim(sim)
#> [1] 101 200