If I am working with the ARMA(1,3) model $$Y_t=Y_{t-1} + \epsilon_t + 0.9\epsilon_{t-3}$$ Where Y's are the observations and $\epsilon$ is a white noise process. I can decompose and find the lag polynomial of the AR part $A(L) = (1-L)$ which means that A(L) has a unit root and therefore is NOT stationary. If I difference the equation using $\Delta(Y_t) = Y_t - T_{t-1}$ to get $$\Delta(Y_t) = \epsilon_t + 0.9\epsilon_{t-3}$$ Im not sure why this process is now stationary? Is it because there is no lag polynomial to have a unit root? Are all AR processess with no lags in $Y_t$ stationary? Is it the case that if the whole lag polynomial is equal to 1 then we have stationarity? Thanks in advance for any help offered.
1 Answer
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I have found the answer to my own question :@ If the lag polynomial A(L)=1 Then we have stationarity in the ARMA model. Hope this helps someone else in the future!