my question is: How can I formulate ARIMA(1,1,1) as Markov Process by extended state space? i.e. if $$s_t = \mu + \sum_{i=1}^p\beta_i s_{t-i} + \varepsilon_t$$ Define$$S_t = (s_t,\ldots,s_{t-p+1})$$ to be extended state. There exists a $F$, such that $$S_{t+1} = F(S_t) + \varepsilon_{t+1},$$ becomes Markov process
I am trying to transform $\Delta Y_t = \alpha_1 \Delta Y_{t-1} + \epsilon_t + \beta_1\epsilon_{t-1}$ equation by same trick. But I am stuck how to handle error terms so that I can view it as a markov chain. Thank you
