The law of the iterated logarithm for non-instantaneous filters of strongly dependent Gaussian sequences
Let \(\{X_n\}\) be a stationary Gaussian sequence, \(H = H(X_{t_1}, \ldots, X_{t_d})\) a \(d\)-dimensional filter with mean zero, \(\theta\) the shift operator and \(S_N = \sum^N_1 H \circ \theta^n\). It is shown that the upper-half law of the iterated logarithm holds for \(S_N\) under suitable conditions on the Hermite rank of \(H\) and the covariance function of \(\{X_n\}\).
scientific article; zbMATH DE number 757600