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A class of modified high‐order autoregressive models with improved resolution of low‐frequency cycles

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  • Alex S. Morton
  • Granville Tunnicliffe‐Wilson

Abstract

. 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 pth order AR models obtained by the addition of a pre‐specified pth 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.

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  • Alex S. Morton & Granville Tunnicliffe‐Wilson, 2004. "A class of modified high‐order autoregressive models with improved resolution of low‐frequency cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 235-250, March.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:2:p:235-250
    DOI: 10.1046/j.0143-9782.2003.00347.x
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    Cited by:

    1. Cecilia Frale & Massimiliano Marcellino & Gian Luigi Mazzi & Tommaso Proietti, 2010. "Survey data as coincident or leading indicators," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 109-131.
    2. Pollock, D.S.G., 2018. "Stochastic processes of limited frequency and the effects of oversampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 18-29.

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