ts-models-ARCH1 {quantspec}

Simulation of an ARCH(1) time series.

Description

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

Y_t = Z_t \sigma_t, \quad \sigma_t^2 = a_0 + a_1 Y_{t-1}^2 + \epsilon_t

where a_0 and a_1 are parameters and \epsilon_t is independent white noise with marginal distribution specified by the parameter innov.

Usage

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.

Value

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

Examples

plot(ARCH1(100, a0=1/1.9, a1=0.9), type="l")