Functional estimation in discrete-time processes

In applications, observed variables are often correlated. For example, X ₁ ,..., X _n may represent the rate of the euro against the dollar on days 1,..., n or the temperature observed in Paris on those same days at midday. We then say that the sequence (X _n , n ≥ 1) is a discrete-time process.

If the X _i have the same unknown density distribution f, kernel or projection density estimators can be constructed. These estimators will remain effective if the process has properties of "asymptotic independence", in other words X _m and X _n are "almost" independent when