Random sampling of long-memory stationary processe

TL;DR

This paper explores how random and deterministic sampling affect the long-memory properties of stationary processes, revealing conditions under which long-memory can vanish and when spectral density is preserved.

Contribution

It demonstrates that long-memory can disappear under heavy-tailed sampling laws and establishes conditions for spectral density preservation during random sampling.

Findings

Long-memory can vanish with heavy-tailed sampling laws.

Spectral density is preserved under general sampling conditions.

Deterministic sampling impacts seasonal long-memory.

Abstract

This paper investigates the second order properties of a stationary process after random sampling. While a short memory process gives always rise to a short memory one, we prove that long-memory can disappear when the sampling law has heavy enough tails. We prove that under rather general conditions the existence of the spectral density is preserved by random sampling. We also investigate the effects of deterministic sampling on seasonal long-memory.