The UCM Procedure

Overview: UCM Procedure

The UCM procedure analyzes and forecasts equally spaced univariate time series data by using an unobserved components model (UCM). The UCMs are also called structural models in the time series literature. A UCM decomposes the response series into components such as trend, seasonals, cycles, and the regression effects due to predictor series. The components in the model are supposed to capture the salient features of the series that are useful in explaining and predicting its behavior. Harvey (1989) is a good reference for time series modeling that uses the UCMs. Harvey calls the components in a UCM the "stylized facts" about the series under consideration. Traditionally, the ARIMA models and, to some limited extent, the exponential smoothing models have been the main tools in the analysis of this type of time series data. It is fair to say that the UCMs capture the versatility of the ARIMA models while possessing the interpretability of the smoothing models. A thorough discussion of the correspondence between the ARIMA models and the UCMs, and the relative merits of UCM and ARIMA modeling, is given in Harvey (1989). The UCMs are also very similar to another set of models, called the dynamic models, that are popular in the Bayesian time series literature (West and Harrison, 1999). In SAS/ETS, you can use PROC SSM for multivariate (and more general univariate) UCMs (see Chapter 27: The SSM Procedure), PROC ARIMA for ARIMA modeling (see Chapter 7: The ARIMA Procedure), PROC ESM for exponential smoothing modeling (see Chapter 14: The ESM Procedure), and the Time Series Forecasting System for a point-and-click interface to ARIMA and exponential smoothing modeling.

You can use the UCM procedure to fit a wide range of UCMs that can incorporate complex trend, seasonal, and cyclical patterns and can include multiple predictors. It provides a variety of diagnostic tools to assess the fitted model and to suggest the possible extensions or modifications. The components in the UCM provide a succinct description of the underlying mechanism governing the series. You can print, save, or plot the estimates of these component series. Along with the standard forecast and residual plots, the study of these component plots is an essential part of time series analysis using the UCMs. Once a suitable UCM is found for the series under consideration, it can be used for a variety of purposes. For example, it can be used for the following:

• forecasting the values of the response series and the component series in the model

• obtaining a model-based seasonal decomposition of the series

• obtaining a "denoised" version and interpolating the missing values of the response series in the historical period

• obtaining the full sample or "smoothed" estimates of the component series in the model