AR(p) reparameterization

[Roulh]

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

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y(t)=a_1 y(t-1)+a_2 y(t-2)+epsilon(t), where epsilon~N(0,1) (1)

I know that if π(.) is the partial autocorrelation, we have that

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a_1=π(1)*[1-π(2)] and a_2=π(2)

By saying that we reparameterize the AR process, we mean that instead of using the relation (1) we use the following

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y(t)=π(1)*[1-π(2)]y(t-1)+π(2)y(t-2)+epsilon(t),

Please help me.