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. We also discuss some questions concerning tapered Toeplitz matrices and operators, central limit theorems for tapered Toeplitz type quadratic functionals, and tapered Fejér-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 Lévy-driven linear processes with memory.