Estimation of cyclic long‐memory parameters

Abstract

This paper studies cyclic long‐memory processes with Gegenbauer‐type spectral densities. For a semiparametric statistical model, new simultaneous estimates for singularity location and long‐memory parameters are proposed. This generalized filtered method‐of‐moments approach is based on general filter transforms that include wavelet transformations as a particular case. It is proved that the estimates are almost surely convergent to the true values of parameters. Solutions of the estimation equations are studied, and adjusted statistics are proposed. Monte‐Carlo study results are presented to confirm the theoretical findings.

Asymptotic normality of simultaneous estimators of cyclic long-memory processes

“…This paper further develops the approach from [2]. Now we obtain asymptotic normality of the proposed estimators.…”

“…Time series with cyclic long-memory behaviours attracted increasing attention in recent years, see [2,3,4,5,15] and the references therein. It was due to importance of such time series in finance, hydrology, cosmology, internet modelling, and other applications to data with non-seasonal cyclicities, see [3,4,6,13,18,32].…”

“…To avoid repetitions, we refer the readers to very detailed motivation, discussion and various examples in [2].…”

“…The publication [2] proposed a new methodology for simultaneous estimation of cyclic and long-memory parameters. It used filter transformations of functional time series.…”

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Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered method-of-moments approach to simultaneously estimate singularity location and long-memory parameters. This paper continues studies of these simultaneous estimators.

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