NONPARAMETRIC FUNCTION ESTIMATION FOR TIME-SERIES BY LOCAL AVERAGE ESTIMATORS

Let (X(t), Y(t)) be a stationary time series with X(t) being R(d)-valu ed and Y(t) real valued, and where Y(t) is not necessarily bounded. Le t E(Y0\X0) be the conditional mean function. Under appropriate regular ity conditions, local average estimators of this function can be chose n to achieve the optimal rate of convergence (n-1 log n)1/(d+2) in L(i nfinity) norm restricted to a compact. The result answers a question r aised by Truong and Stone.