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Biometrika 1980 67(2):365-373; doi:10.1093/biomet/67.2.365
© 1980 by Biometrika Trust
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Hidden periodic autoregressiye-moving average models in time series data

G. C. TIAO and M. R. GRUPE

Department of Statistics, University of Wisconsin Madison
Federal Reserve Board Washington, D.C.

Some properties of a class of periodic models for characterizing seasonal time series are explored. The relationships between periodic models and multiple autoregressive-moving average models are developed and used to gain insight into the behaviour of periodic models. In particular it is shown how homogeneous autoregressive-moving average models may be mistakenly specified for series in which periodic properties are present. Consequences of such misspecification on forecasting and diagnostic checking are also derived.

Key Words: Autoregressive-moving average model • Forecast efficiency • Periodic model • Seasonal model • Timeseries.


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