Marginal density estimation for linear processes with cyclical long memory

TL;DR

This paper extends kernel density estimation convergence results to linear processes with cyclical long memory, where spectral density singularities are not only at zero, affecting convergence rates and limit distributions.

Contribution

It generalizes previous results to stationary processes with spectral singularities beyond the origin, revealing new convergence behaviors.

Findings

Convergence rates differ from classical cases.

Limit distributions are affected by spectral singularities.

Extends theoretical understanding of density estimation in cyclical processes.

Abstract

Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for which the singularities of the spectral density are not limited to the origin. We show that the convergence rates and the limit distribution may be different in this context.