Autoregressive Moving-Average Simulation (First Order)

a1

0.4

b1

0.4

randomize

This Demonstration shows realizations of a first-order ARMA process

y

, using the random variable

r

drawn from a normal density with mean zero and variance unity. It is governed by the equation:

y

i

=a

y

i-1

+b

r

i-1

+

r

i

,

i=1,…,N

where

N

is the length of the series.

The constant

a

is the autoregressive constant (

-1<a<1

), and the constant

b

is the moving-average constant (

0<b<1

). A series of length 400 is created in every case.