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A time series given by following

$$X_{t-3} – 2.5X_{t-2} + 2X_{t-1} – 0.5X_{t} = E(t) $$

Can you fit an $\text{ARIMA}(p,d,q)$ model in this ?

I tried bring the $X(t)$ term on the right hand side and dividing the entire equation by its coefficient $0.5$. Don't know what to do next.

$E(t)$ is Random White Noise.

Tianlalu
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avi selot
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    I am afraid that no amount of differencing is going to reveal a causal $\operatorname{ARMA}$ process. You may note that by symmetry of the white noise process, $-2E_t \stackrel d=\widetilde E_t$, where $\widetilde E_t$ is also a white noise process with $\operatorname{Var}(\widetilde E_t) = 4\operatorname{Var(E_t)}$, so if the process was to be an $\operatorname{ARIMA}$ process, it would be an $\operatorname{ARIMA}(3,d,0)$ process. I suppose I can show my work of differencing the process up to 5 times before halting. I suppose you could prove that no $d\in\mathbb N$ exists, if you wanted. – Therkel Dec 13 '16 at 09:35

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