Periodic Time Series Models

Periodic Time Series Models

Periodic Time Series Models

Periodic Time Series Models


This book considers periodic time series models for seasonal data, characterized by parameters that differ across the seasons, and focuses on their usefulness for out-of-sample forecasting. Providing an up-to-date survey of the recent developments in periodic time series, the book presents alarge number of empirical results. The first part of the book deals with model selection, diagnostic checking and forecasting of univariate periodic autoregressive models. Tests for periodic integration, are discussed, and an extensive discussion of the role of deterministic regressors in testing for periodic integration and inforecasting is provided. The second part discusses multivariate periodic autoregressive models. It provides an overview of periodic cointegration models, as these are the most relevant. This overview contains single-equation type tests and a full-system approach based on generalized method of moments. All methods are illustrated with extensive examples, and the book will be of interest to advanced graduate students and researchers in econometrics, as well as practitioners looking for an understanding of how to approach seasonal data.


This book deals with the analysis of economic time series with seasonality. There are many ways to model such series, where typically these models are to be used for out-of-sample forecasting. One class of models for seasonal series is the periodic time series model, and this class is the focus of the present book.

In a sense, our book can be seen as a second edition, or better, an updated edition, of Periodicity and Stochastic Trends in Economic Time Series, which was written by the first author and which was published in 1996, also by Oxford University Press. At that time, there were not many academics and practitioners who considered periodic models for their seasonal time series. Hence, the 1996 book aimed to provide arguments as to why periodic models could be useful. the first few chapters considered (seasonal) time series in general, and Chapter 6 in that book was meant to argue that perhaps it would be better to use periodic models, instead of the, at the time, popular models.

We believe that the current book no longer needs all these chapters. a casual look at the relevant literature suggests that periodic models are now accepted as a useful tool, although perhaps not implemented by many. Indeed, a recent more theoretical book on seasonality, The Econometric Analysis of Seasonal Time Series by Eric Ghysels and Denise Osborn (Cambridge University Press, 2001), dedicates an entire chapter to periodic models. As the authors state, that chapter discusses part of the theory, and therefore we will aim to give a more complete account, as well as to give ample empirical illustrations. Hence, one might view our book as a cookbook, which guides the reader towards the eventual empirical use of a periodic time series model.

Our book gives a review of everything we now know about periodic time series models. It summarizes a decade of research, and we currently believe that everything that is needed to be understood is now understood, although there are a few avenues for further research. in part, we ourselves contributed to the literature on periodic models, where we sometimes had the help of our co-authors Peter Boswijk, Jörg Breitung, Niels Haldrup, Frank Kleibergen, Gary Koop, and Marius Ooms. We are extremely grateful for their input.

This book will be most useful for readers who are interested in obtaining a comprehensive picture of periodic time series modeling. the list of references is up to date. the book can also be useful for readers who want to apply the

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