Hidden Periodic Autoregressive-Moving Average Models in Time Series Data

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Abstract
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 behavior 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. [Applicability to data on air pollution was discussed].

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