We consider the problem of predicting values of a random process or field satisfying a linear model y(x)=θ⊤f(x)+ε(x), where errors ε(x)are correlated. This is a common problem in kriging, where the case of discrete observations is standard. By focussing on the case of continuous...

We introduce a two-step procedure for more efficient nonparametric prediction of a strictly stationary process admitting an ARMA representation. The procedure is based on the estimation of the ARMA representation, followed by a nonparametric regression where the ARMA residuals are used as...

In a typical empirical modeling context, the data generating process (DGP) of a time series is assumed to be known up to a finite-dimensional parameter. In such cases, Rissanen's (1986) theorem provides a lower bound for the empirically achievable distance between all possible data-based models...