Seasonal Models

  • Mike West
  • Jeff Harrison
Part of the Springer Series in Statistics book series (SSS)


Cyclical or periodic behaviour is evident in many time series associated with economic, commercial, physical and biological systems. Annual seasonal cycles, for example, are well accepted as providing the basis of the agricultural calendar. Each year the earth revolves about the sun, the relative positions of the two bodies determining the earth’s climatic conditions at any time. This natural cycle is essentially uncontrollable and has to be accepted. It is important to recognise the induced seasonally in, for example, the demand for agricultural goods and many other products, and to include it as a factor in any forecasting model. Such seasonal patterns may have enormous implications for stock control and production planning in agricultural business; it is not uncommon, for example, to encounter demand patterns exhibiting seasonal peak to trough ratios of order of 20 to 1. Various other annual cycles, such as demand for fireworks, Valentine cards, Easter eggs and so forth, are even more pronounced. Although many such annual patterns arise from the natural solar cycle, not all do, nor is the effect always controllable. One example concerns the demand for an anaesthetic whose annual cycle initially surprised the marketing department of the manufacturing company. Upon closer investigation it was found that most of the seasonality was quarterly, coinciding with the quarterly accounting periods of the hospitals to whom most of the anaesthetic was sold. Similar seasonal patterns of demand and sales arise partially as responses to advertising effort and expenditure, campaigns being repeated along similar lines from year to year. In addition to identifying and anticipating cycles of this sort, decision makers may wish to exert control in attempts to alter and, particularly, reduce seasonal fluctuations. In commercial environments this is often desirable to reduce inefficiencies in the use of manufacturing plant and warehouse facilities. One particular example concerns the increase in milk prices that is designed to encourage producers to keep more cows over winter when feed costs are high, thus dampening seasonal fluctuations in milk supplies.


Seasonal Pattern Discount Factor Fourier Coefficient Harmonic Component Seasonal Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • Mike West
    • 1
  • Jeff Harrison
    • 2
  1. 1.Institute of Statistics and Decision SciencesDuke UniversityDurhamUSA
  2. 2.Department of StatisticsUniversity of WarwickCoventryUK

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