Estimating a variance function of a nonstationary process

Abstract

Non-constant variance functions are a common feature in geophysical processes, and estimating the variance function is important to provide accurate prediction intervals. We propose a nonparametric approach to estimating the variance function from a single continuous-space process where the mean function is smooth and the additive errors are correlated and heteroskedastic. We explore a few configurations of difference filters and recommend filter weights depending on the strength of the correlation in the error process. Symmetric-weight filters are preferred when the errors are strongly correlated, and Hall–Kay–Titterington weight filters are preferred when the errors are weakly correlated or independent. The proposed method provides efficiency in computing, especially with strongly correlated data.