Chapter

Periodic models for trending data

Philip Hans Franses and Richard Paap

in Periodic Time Series Models

Published in print March 2004 | ISBN: 9780199242023
Published online August 2004 | e-ISBN: 9780191601286 | DOI: http://dx.doi.org/10.1093/019924202X.003.0004

Series: Advanced Texts in Econometrics

 Periodic models for trending data

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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

Chapter.  18990 words. 

Subjects: Econometrics and Mathematical Economics

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