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A class of modified high‐order autoregressive models with improved resolution of low‐frequency cycles
Author(s) -
Morton Alex S.,
TunnicliffeWilson Granville
Publication year - 2004
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 - 10.1046/j.0143-9782.2003.00347.x
Subject(s) - autoregressive model , mathematics , star model , class (philosophy) , simple (philosophy) , process (computing) , spectral density , power (physics) , order (exchange) , spectral density estimation , mathematical optimization , algorithm , autoregressive integrated moving average , econometrics , statistics , computer science , time series , mathematical analysis , artificial intelligence , fourier transform , philosophy , physics , epistemology , finance , quantum mechanics , economics , operating system
. We consider regularly sampled processes that have most of their spectral power at low frequencies. A simple example of such a process is used to demonstrate that the standard autoregressive (AR) model, with its order selected by an information criterion, can provide a poor approximation to the process. In particular, it can result in poor multi‐step predictions. We propose instead the use of a class of p th order AR models obtained by the addition of a pre‐specified p th order moving average term. We present a re‐parameterization of this model and show that with a low order it can provide a very good approximation to the process and its multi‐step predictions. Methods of model identification and estimation are presented, based on a transformed sample spectrum, and modified partial autocorrelations. The method is also illustrated on a real example.