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In Tsay's Financial Time Series, for a AR(p) process,

In the time series literature, inverses of the two solutions (to the characteristic equation of AR(2)) are referred to as the characteristic roots of the AR(2) model.

From other areas of mathematics where the concept of characteristic equations also exists, e.g. difference equations, differential equation, eigenvalues of matrices, isn't the characteristic roots define as the solutions to the characteristic equations?

If yes, what the book says is very unusual, and confusing. I hope this is not widely used in time series.

kjetil b halvorsen
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Tim
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    Yes, it can be confusing. This is discussed in the comment thread beginning at http://stats.stackexchange.com/questions/27882/what-is-the-difference-between-serial-correlation-and-having-a-unit-root/27890#comment52000_27890. It might help to know that $\lambda$ is a root of the polynomial $p_nx^n+p_{n-1}x^{n-1}+\cdots+p_1x+p_0$ (with $p_0\ne 0\ne p_n$) if and only if $1/\lambda$ is a root of $p_n+p_{n-1}x+p_{n-2}x^2+\cdots+p_1x^{n-1}+p_0 x^n.$ Note, too, that the same relationship holds between $\det(1-\lambda\mathbb{A})$ and $\det(\lambda-\mathbb{A})$ for any matrix $\mathbb{A}$. – whuber Apr 30 '14 at 14:16

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