On filter-type estimation of discretely sampled cyclic long-memory processes

TL;DR

This paper extends the generalized filtered method of moments for cyclic long-memory processes from continuous to discrete sampling, demonstrating strong consistency and similar properties, supported by numerical validation.

Contribution

It introduces a discrete-time adaptation of the method, proving its theoretical properties and providing practical guidelines through numerical experiments.

Findings

Discrete estimates are strongly consistent.

Estimates have similar properties to continuous case.

Sampling rates affect estimation accuracy.

Abstract

The generalized filtered method of moments was developed in the recent papers by Alomari et al., 2020, and Ayache et al., 2022. It used functional data obtained from continuously sampled cyclic long-memory stochastic processes to simultaneously estimate their parameters. However, the majority of applications deal with discretely sampled processes or time series. This paper extends the approach to accommodate discrete-time scenarios. It proves that the new discrete estimates exhibit analogous properties to the continuous case and are strongly consistent with the same rates of convergence. The numerical study results are presented to illustrate the theoretical findings and to indicate the sampling rates and resolution levels required for accurate estimates.