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I've been estimating some non-linear Macroeconomic models.

As a field, do we care about complex roots of the autoregressive matrix? Is there any reason to think the real word processes have real roots?

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As regards dynamic convergence and stability, complex roots are associated either with a stable orbit around the fixed point, or with convergence to the fixed point by damped oscillations.

Check also https://wordpress.com/post/alecospapadopoulos.wordpress.com/197

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