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Autoregressive Polynomial


The autoregressive polynomial, also called the characteristic polynomial, of an AR(p) autoregressive model is

 phi(z)=1-phi_1z-phi_2z^2-...-phi_pz^p.

Its roots determine stability: the usual causal stationary solution exists when every root lies outside the unit circle. For a vector autoregressive model, the corresponding condition uses the roots of det(I-A_1z-...-A_pz^p).


See also

Autoregressive Model, Characteristic Polynomial, Stationary Time Series, Unit Root, Vector Autoregressive Model

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References

Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.

Cite this as:

Weisstein, Eric W. "Autoregressive Polynomial." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AutoregressivePolynomial.html

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