Martingale difference sequence

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In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series Y is an MDS if its expectation with respect to past values of another stochastic series X is zero. Formally

E(Y_{i+1}|X_{i},X_{i-1},\dots)=0 \quad \forall i.

If Z is a martingale, for example, then Yi = Zi − Zi − 1 will be an MDS—hence the name.

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