Essentials of Time Series for Financial Applications

Definition 2.9

(Invertibility)

An invertible MA(q) model can be expressed as an $\mathrm{AR}(\infty )$:

$y_t=\sum _{i=0}^{\infty }{\varphi }_i{L}^i{y}_{t-i}+u_t.$ (2.65)

(2.65)

An MA(q) is invertible when the magnitude of all the roots of the MA polynomial exceeds 1.

Therefore, it is evident that in an invertible MA(q) process, the value of $y_t$ depends on all its previous values, so that the PACF of an MA(q) model will decline geometrically. More in general, the ACF of an MA model has the same shape of ...