One of the most widely used contributions to forecasting methodology arising from the book by Box and Jenkins (Time Series Analysis, Forecasting and Control, Holden-Day, 1970) on Forecasting and Control, is their approach to modeling seasonal time series. Their models are used across the world, not least because they have been incorporated into standard software such as the X12-ARIMA seasonal adjustment package. This chapter will be an exposition of these methods, based on a selection of time series case studies, ranging from the airline series example presented by Box and Jenkins, to an example of half hourly electricity demand. The exposition will not, however, be limited to the approach advocated by Box and Jenkins for identifying these models, which is based on inspecting autocorrelation functions of seasonal and non-seasonal differences of the series. The characteristics of seasonality will first be considered, and other approaches to identifying the model suggested. These arise directly from Box and Jenkins (1970) arguments but were not explicitly promoted in their book. Other considerations of the chapter will be how seasonal ARIMA models characterize the relationship between fixed and variable seasonality, the incorporation of calendar effects and the extension of the Airline model to series with two seasonal periods.


Exponentially Weighted Move Average Sample Spectrum Seasonal Period Difference Series Calendar Effect 
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© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Lancaster UniversityLancasterUK
  2. 2.The Civil Service CollegeLondonUK

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