Definitions

We define ARMA model as

$$w_{t} = \sum_{i=1}^p a_i w_{t-i} +\sum_{i=1}^q b_i \epsilon_{t-i} +\epsilon_t$$ (1)

We assume that

$$z_{t-i}=0,\ w_{t-i}=0,\ \epsilon_{t-i}=0,\ \ if\ \ t \le i.$$ (2)