Martingale difference sequence

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

$E(Y_{i+1}|X_{i},X_{i-1},\dots)=0 \quad \text{for all}~ i.$

If Z is a martingale, for example, then Y_i = Z_i − Z_{i − 1} will be an MDS—hence the name.

References

• James Douglas Hamilton (1994), Time Series Analysis, Princeton University Press. ISBN 0-691-04289-6

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