I am solving an exercise where I am using a martingale difference sequence, so here is my doubt. $\varepsilon_t$ is a stationary and ergodic martingale difference sequence. I get to one point where I have $-\frac{1}{2}\varepsilon_T +\frac{1}{2}\varepsilon_0$ where T is the maximum value of t and 0 is the minimum. Is the result of the difference 0? If yes, could you please explain why?
2026-03-28 09:43:45.1774691025
martingale difference sequence
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