I was reading this passage in a book and I am confused about the last line. As far as I understand, the white noise process does not allow for conditional heteroskedasticity due to its i.i.d. property. However, can somebody explain why a martingale difference sequence allows for conditional heteroskedasticity?
Martingale: The stochastic process $v_t$ is called a martingale sequence if \begin{align*} E(v_t|v_{t−1}, v_{t−2}, . . .) = v_{t−1} \;\forall t. \end{align*} Martingale Difference: $u_t \equiv \triangle v_t$ is called a martingale difference if \begin{align*} E(u_t|v_{t−1}, v_{t−2}, . . .) = 0 \;\forall t \end{align*} Unlike an iid white noise process, a white noise process that is a martingale difference sequence allows for conditional heteroskedasticity.