Martingale difference sequence

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 Yi = ZiZi − 1 will be an MDS—hence the name.

References

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