如何產生具有 ARCH 的殘差項

以比較簡單的 ARCH(1) 為例

e(t) = v(t)* σ(t) =v(t)* [w + α*e(t)^2]^0.5

where

σ(t)^2 = w + α*e(t)^2

v(t) ~ normal(0,1)

gretl 程式:

(假設 smpl full = smpl 1 100)

nulldata 100

setobs 1 1 -t

scalar w=0.5

scalar alpha = 0.8

smpl full

series v=normal()

series e=0

series sigma2 = 0.001 # 先隨便設

smpl 2 100

series e=v*(w + alpha*e(-1)^2)^0.5