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Periodic Time Series Models$
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Philip Hans Franses and Richard Paap

Print publication date: 2004

Print ISBN-13: 9780199242023

Published to Oxford Scholarship Online: August 2004

DOI: 10.1093/019924202X.001.0001

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Periodic models for trending data

Periodic models for trending data

Chapter:
(p.61) 4 Periodic models for trending data
Source:
Periodic Time Series Models
Author(s):

Philip Hans Franses (Contributor Webpage)

Richard Paap (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/019924202X.003.0004

In Chapter 4 we address the issue of how to incorporate descriptions of trends in periodic models. It is well known that the trend in many economic time series may be characterized by a so-called unit root in the autoregressive part of the model, together with a non-zero intercept, although several series allow for a purely deterministic trend. For periodic models, the notions of unit roots and deterministic trends become a little more complicated as there might be different trends across the seasons, thereby, for example, allowing for increasing or decreasing seasonal variation. If a periodic autoregression has a single unit root, this will appear as a function of all parameters in the model. If this restriction does not coincide with the well-known (1,-1) filter, that is, the first-differencing, then the data are periodically integrated. We discuss testing for periodic integration and the role of deterministic terms in periodic models. All material is illustrated using quarterly US industrial production series.

Keywords:   Periodic integration, sequential model building, neglected periodicity

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