Martingale difference sequence
In probability theory, a martingale difference sequence (MDS) is related to the concept of the martingale. A stochastic series X is an MDS if its expectation with respect to the past is zero. Formally, consider an adapted sequence ![\{X_t, \mathcal{F}_t\}_{-\infty}^{\infty}](/Images/godic/202501/26/d7a5e2187311576578785908958041762526.png")
on a probability space ![(\Omega, \mathcal{F}, \mathbb{P})](/Images/godic/202501/26/8b472a66fac3182461fb34f468ce587d2526.png")
. ![X_t](/Images/godic/202501/26/417748f905fcf618688a30338c8c6e102527.png")
is an MDS if it satisfies the following two conditions: