(Armenian Academy of Sciences, 2021)
M. S. Ginovyan; A. A. Sahakyan
In this paper, we survey some recent results on parametric and nonparametric statistical
estimation about the spectrum of stationary models with tapered data, as well as, a question
concerning robustness of inferences, carried out on a linear stationary process contaminated by a
small trend. We also discuss some questions concerning tapered Toeplitz matrices and operators,
central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fejer-type ´
singular integrals. These are the main tools for obtaining the corres ponding results, and also
are of interest in themselves. The processes considered will be discrete- time and continuous-time
Gaussian, linear or Levy-driven linear processes with memory.