By Philip H. Franses

ISBN-10: 019924202X

ISBN-13: 9780199242023

ISBN-10: 0199242038

ISBN-13: 9780199242030

ISBN-10: 1429420375

ISBN-13: 9781429420372

During this sleek research of using periodic types within the description and forecasting of financial facts the authors examine such components as seasonal time sequence, periodic time sequence types, periodic integration and periodic cointegration.

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**Sample text**

For PAR processes of higher order, this may however become analytically cumbersome. 10), is then more convenient. This method is also used in Bentarzi and Hallin (1994) for the analysis of the invertibility of a PMA process. 26) are on the unit circle, the YT process, and also the yt process, have k unit roots. Indeed, it is important to understand (in order to avoid serious misinterpretation) that the number of unit roots in yt equals that in YT, and hence that no additional unit roots are introduced in the multivariate representation.

Note, however, that the number of lags for most variables, in order for the estimated residuals to behave a bit like a white-noise-type error process, is quite large. As will become clear in Chapter 3, this might also be a sign of the usefulness of periodic models, as neglecting periodicity leads to many lags in non-periodic models. 2 Typical features of seasonal time series The graphical and basic regression results in the previous section indicated that the data have a trend, and that many of the fourteen series show substantial 18 Properties of seasonal time series seasonal variation, while only a few show seasonal heteroskedasticity.

In summary, we find evidence of periodic patterns in nine of the fourteen series. Interestingly, the non-periodic tests do not find evidence of neglected seasonality, while the periodic tests do, which can be seen from comparing the p values for FpseT with those of FseT. Simulation results in Franses (19956) imply that non-periodic tests have a low ability to indicate whether the series are perhaps better described by a periodic model. Therefore, in order to test for remaining or neglected seasonality, we recommend the use of a test based on a periodic model.

### Periodic Time Series Models (Advanced Texts in Econometrics) by Philip H. Franses

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