I'm no expert in the notion of stability but I think Bartlett means all roots outside the unit circle and wikipedia is just incorrectly stated.

Note though that you need to be careful how you define the polynomial. Take for example, the AR(2). $ y_t = \phi_1 y_{t-1} + \phi_2 y_{t-2} + e_t $.

Then the AR(2) polynomial can be defined as $ (1 - \phi_1 \lambda - \phi_2 \lambda^2) $ or as $ (z^2 - \phi_1 z - \phi_2)$.

These two polynomials have roots that are reriprocals of each other. In the first case, the AR(2) is stable if the roots are inside the unit circle. In the second case, the AR(2) is stable if the roots are outside the unit circle. So be careful how you define the polynomial before deciding on the statement. For me. its more natural to define it with the z's.

All of this is in Hamilton's text which I highly recommend.

I'm no expert in the notion of stability but I think Bartlett means all roots outside the unit circle and wikipedia is just incorrectly stated.

Note though that you need to be careful how you define the polynomial. Take for example, the AR(2). $ y_t = \phi_1 y_{t-1} + \phi_2 y_{t-2} + e_t $.

Then the AR(2) polynomial can be defined as $ (\lambda^2 - \phi_1 \lambda - \phi_2) $ or as $ (1 - \phi_1 z - \phi_2 z^2)$.

These two polynomials have roots that are reriprocals of each other. In the first case, the AR(2) is stable if the roots are inside the unit circle. In the second case, the AR(2) is stable if the roots are outside the unit circle. So be careful how you define the polynomial before deciding on the statement. For me. its more natural to define it with the z's.

All of this is in Hamilton's text which I highly recommend.