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Semiparametric Inference in Seasonal and Cyclical Long Memory Processes
Author(s) -
Arteche Josu,
Robinson Peter M.
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00170
Subject(s) - mathematics , long memory , range (aeronautics) , monte carlo method , gaussian , symmetry (geometry) , series (stratigraphy) , statistical physics , spectral density , inference , spectrum (functional analysis) , inflation (cosmology) , periodogram , zero (linguistics) , econometrics , statistics , computer science , physics , volatility (finance) , paleontology , linguistics , materials science , geometry , philosophy , quantum mechanics , artificial intelligence , theoretical physics , composite material , biology
Several semiparametric estimates of the memory parameter in standard long memory time series are now available. They consider only local behaviour of the spectrum near zero frequency, about which the spectrum is symmetric. However long‐range dependence can appear as a spectral pole at any Nyqvist frequency (reflecting seasonal or cyclical long‐memory), where the spectrum need display no such symmetry. We introduce Seasonal/Cyclical Asymmetric Long Memory (SCALM) processes that allow differing rates of increase on either side of such a pole. To estimate the two consequent memory parameters we extend two semiparametric methods that were proposed for the standard case of a spectrum diverging at the origin, namely the log‐periodogram and Gaussian or Whittle methods. We also provide three tests of symmetry. Monte Carlo analysis of finite sample behaviour and an empirical application to UK inflation data are included. Our models and methods allow also for the possibility of negative dependence, described by a possibly asymmetric spectral zero.