In Giraitis, Robinson, and Samarov (1997), we have shown that the optimal rate for memory parameter estimators in semiparametric long memory models with degree of "local smoothness" [beta] is n-r([beta]), r([beta])=[beta]/(2[beta]+1), and that a log-periodogram regression estimator (a modified...

A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved....

We introduce a new statistic written as a sum of certain ratios of second-order increments of partial sums process of observations, which we call the increment ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for d-integrated () behavior of time series Xt,...

We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in Giraitis et al. [L. Giraitis, R. Leipus, A. Philippe, A test for stationarity versus trends and unit roots for a wide class of dependent errors,...