$\varepsilon_{1j}, \varepsilon_{2j}, \varepsilon_{3j} ∼ iid(0; 1)$ and they are three independent processes.
$ y_{t} =x\sum_{i=1}^{t}\sum_{j=1}^{i} \varepsilon_{1j} + y\sum_{i=1}^{t} \varepsilon_{2i} + \varepsilon_{3t}$
$x$, $y$ are non-zero constants.
How to find the order of integration $ y_{t} $?
I think it is $I(2)$. But I am not sure how to prove it. Would "constant mean and variance" for all $t$ enough to prove that the difference are stationary? If not, how to prove that the autocovariance is constant for all $t$?
Are there better ways to prove that e.g. the second difference of $ y_{t} $ is stationary?