ts-models-ARCH1 function

Simulation of an ARCH(1) time series.

Simulation of an ARCH(1) time series.

Returns a simulated time series (Yt)(Y_t) that fulfills the following equation: [REMOVE_ME]Yt=Ztσt,σt2=a0+a1Yt12+ϵt[REMOVEME2] Y_t = Z_t \sigma_t, \quad \sigma_t^2 = a_0 + a_1 Y_{t-1}^2 + \epsilon_t [REMOVE_ME_2]

where a0a_0 and a1a_1 are parameters and ϵt\epsilon_t is independent white noise with marginal distribution specified by the parameter innov.

ARCH1(n, a0, a1, overhead = 500, innov = rnorm)

Arguments

  • n: length of the time series to be returned

  • a0: parameter

  • a1: parameter

  • overhead: an integer specifying the ``warmup'' period to reach an approximate stationary start for the times series

  • innov: a function with one parameter n that yields n

    independent pseudo random numbers each time it is called.

Returns

Return an ARCH(1) time series with specified parameters.

Description

Returns a simulated time series (Yt)(Y_t) that fulfills the following equation:

Yt=Ztσt,σt2=a0+a1Yt12+ϵt Y_t = Z_t \sigma_t, \quad \sigma_t^2 = a_0 + a_1 Y_{t-1}^2 + \epsilon_t

where a0a_0 and a1a_1 are parameters and ϵt\epsilon_t is independent white noise with marginal distribution specified by the parameter innov.

Examples

plot(ARCH1(100, a0=1/1.9, a1=0.9), type="l")
  • Maintainer: Tobias Kley
  • License: GPL (>= 2)
  • Last published: 2024-07-11