Weakly Dependent

Definition: A time series process {x_t} is weakly dependent iff these four conditions hold:

1. {x_t} is essentially stationary, that is if E[x_t²] is uniformly bounded. In any such process, the following 'variance of partial sums' is well defined, and it will be used in the following conditions. Define s_T² to be the variance of the sum from t=1 to t=T of x_t.
2. s_T² is O(T).
3. s_T^-2 is O(1/T).
4. The asymptotic distribution of the sum from t=1 to t=T of (x_t-E(x_t))/s_T is N(0,1).

These conditions rule out random processes which are serially correlated too positively or negatively or whose partial sums are near zero.

(Econterms)

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