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Estimation of cyclic long‐memory parameters
Author(s) -
Alomari Huda Mohammed,
Ayache Antoine,
Fradon Myriam,
Olenko Andriy
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12404
Subject(s) - mathematics , long memory , singularity , monte carlo method , wavelet , statistics , econometrics , mathematical analysis , artificial intelligence , computer science , volatility (finance)
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.