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Structural Time Series Modeling and Forecasting

The UCM procedure provides a flexible environment for analyzing time series data using structural time series models, also called unobserved components models (UCM). These models represent the observed series as a sum of suitably chosen components such as trend, seasonal, cyclical, and regression effects. You can use the UCM procedure to formulate comprehensive models that bring out all the salient features of the series under consideration. Structural models are applicable in the same situations where Box-Jenkins ARIMA models are applicable; however, the structural models tend to be more informative about the underlying stochastic structure of the series. The UCM procedure includes the following features:

  • general unobserved components modeling where the models can include trend, multiple seasons and cycles, and regression effects

  • maximum-likelihood estimation of the model parameters

  • model diagnostics that include a variety of goodness-of-fit statistics, and extensive graphical diagnosis of the model residuals

  • forecasts and confidence limits for the series and all the model components

  • Model-based seasonal decomposition

  • extensive plotting capability that includes the following:

    • forecast and confidence interval plots for the series and model components such as trend, cycles, and seasons

    • diagnostic plots such as residual plot, residual autocorrelation plots, and so on

    • seasonal decomposition plots such as trend, trend plus cycles, trend plus cycles plus seasons, and so on

  • model-based interpolation of series missing values

  • full sample (also called smoothed) estimates of the model components

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