Spectral density estimation through a regularized inverse problem

Summary. In the study of stationary processes on the real line, the spectral den- sity function is a parameter of considerable interest. In this paper, we consider a new estimator of the spectral density function obtained by a regularized inversion of estimated covariances. In particular, the data are not required to be observed on a grid and the estimator is not based on the periodogram. For data that are observed on a grid, the estimator is derived in closed from, and the mean squared error of the estimator can be computed. A numerical study is also included to illustrate the methodology. Running title: Spectrum estimation through a regularized inverse problem