Martingale difference sequence
Encyclopedia
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
If
is a martingale, for example, then 
will be an MDS—hence the name.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, a martingale difference sequence (MDS) is related to the concept of the martingale
Martingale (probability theory)
In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
. A stochastic series
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...
Y is an MDS if its expectation
Expected value
In probability theory, the expected value of a random variable is the weighted average of all possible values that this random variable can take on...
with respect to past values of another stochastic series X is zero. Formally
If
is a martingale, for example, then will be an MDS—hence the name.