Statistical inference for stationary linear models with tapered data

In this paper, we survey some recent results on statistical inference (parametric and nonparametric statistical estimation, hypotheses testing) 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 question concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fejer-type kernels and singular integrals. These are the main tools for obtaining the corresponding 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.