AR(p) reparameterization
Posted: Sat Sep 14, 2013 11:11 am
Hi!
I read the attached paper. The main idea of this paper is to reparametize the autoregressive process using the partial autocorrelation function. I would like to ask, if someone could give me an example. Lets assume than we have the AR(2) process
I know that if π(.) is the partial autocorrelation, we have that
By saying that we reparameterize the AR process, we mean that instead of using the relation (1) we use the following
Please help me.
I read the attached paper. The main idea of this paper is to reparametize the autoregressive process using the partial autocorrelation function. I would like to ask, if someone could give me an example. Lets assume than we have the AR(2) process
Code: Select all
y(t)=a_1 y(t-1)+a_2 y(t-2)+epsilon(t), where epsilon~N(0,1) (1)Code: Select all
a_1=π(1)*[1-π(2)] and a_2=π(2)Code: Select all
y(t)=π(1)*[1-π(2)]y(t-1)+π(2)y(t-2)+epsilon(t),