The paper obtains the general form of the cross-covariance function of vector fractional Brownian motions with correlated components having different self-similarity indices.

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclic effects. In particular, we extend the results of Ho and Hsing (1996), Mielniczuk (1997) and Hall and Hart (1990) to the stationary processes for which the singularities of the spectral...

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,...

In the doctoral dissertation, we consider problems of testing and estimating changed segment with unknown starting position and duration of epidemic state in the autoregressive first-order model. The proposed tests are based on partial sums of model residuals and model-parameter...

Disertacijoje nagrinėjamas pirmos eilės autoregresinio modelio pasikeitusio segmento testavimo ir vertinimo uždavinys. Aprašomo modelio epideminio pasikeitimo pradžia ir ilgis nėra žinomi. Pasiūlyti kriterijai pasikeitusio segmento testavimui, kurie pagrįsti modelio paklaidų...