Monotone spectral density estimation

TL;DR

This paper introduces two new estimators for monotone spectral density based on isotonic regression of the periodogram and log-periodogram, providing theoretical properties and optimality results.

Contribution

It develops and analyzes two novel monotone spectral density estimators using isotonic regression, with proven limit distributions and rate optimality for different process types.

Findings

Estimators are rate optimal for short and long memory processes.

Derived pointwise limit distribution results for both estimators.

Applicable to linear and Gaussian processes.

Abstract

We propose two estimators of a monotone spectral density, that are based on the periodogram. These are the isotonic regression of the periodogram and the isotonic regression of the log-periodogram. We derive pointwise limit distribution results for the proposed estimators for short memory linear processes and long memory Gaussian processes and also that the estimators are rate optimal.