Forecasting time series with increasing seasonal variation

Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function‐type ARIMA models employing seasonal dummy variables. An explanation is given for th...

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Bibliographic Details
Published inJournal of forecasting Vol. 9; no. 5; pp. 419 - 436
Main Authors Bowerman, Bruce L., Koehler, Anne'b., Pack, David J.
Format Journal Article
LanguageEnglish
Published Chichester John Wiley & Sons, Ltd 01.10.1990
Wiley
Wiley Periodicals Inc
Subjects
ARIMA Box-Jenkins modeling
Economic models
Forecasting
Forecasting techniques
Maximum likelihood estimation
Prediction intervals
Seasonal
Seasonal fluctuations
Seasonality
Studies
Time series
Time series forecasting
Transformations
Variation
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Summary:Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function‐type ARIMA models employing seasonal dummy variables. An explanation is given for the typical ARIMA model identification analysis failing to identify double seasonal difference models for this kind of data. A logical process of selecting one option for a particular case is outlined, focusing on issues of linear versus non‐linear increasing seasonal variation, and the level of stochastic versus deterministic behavior in a time series. Example models for the various options are presented for six time series, with point forecast and interval forecast comparisons. Interval forecasts from data‐transformation models are found to generally be too wide and sometimes illogical in the dependence of their width on the point forecast level. Suspicion that maximum likelihood estimation of ARIMA models leads to excessive indications of unit roots in seasonal moving‐average operators is reported.
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ArticleID:FOR3980090502
George and Mildred Panuska Professor of Business Administration and Chair of Decision Sciences at Miami University (Ohio). She received an AB, AM and PhD in mathematics from Indiana University. Her publications include articles in Proceedings of the American Mathematical Society, Mathematics Annalen, Quarferly Journal of Marhematics, Communications in Statistics, Decision Sciences, and the International Journal of Forecasting.
Professor of Decision Sciences at Miami University (Ohio). He received his PhD in statistics from Iowa State University. His research interests include forecasting and applied statistics, and he has published over twenty articles on these topics. Dr Bowerman co‐authored Time Series Forecasting: A n Applied Approach, which earned an Outstanding Academic Book Award from Choice magazine, and three other books.
Associate Professor of Decision Sciences at Miami University (Ohio). He earned his PhD in Business Statistics from the University of Wisconsin‐Madison in 1973 and has provided some of the first computer software for the ARIMA model time series forecasting method. Dr Pack has published papers in the Journal of Forecasting, Decision Sciences, and Management Science.
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ISSN:0277-6693
1099-131X
DOI:10.1002/for.3980090502