Unobserved components model (UCM)
Stata’s new ucm command estimates the parameters of an unobserved
components model (UCM). UCM decomposes a time series into trend,
seasonal, cyclical, and idiosyncratic components and allows for exogenous
variables. UCM is an alternative to ARIMA models and provides a flexible
and formal approach to smoothing and decomposition problems.
Here we fit monthly data on the median duration of unemployment spells in
the United States to a stochastic cycle model with a stochastic seasonal
component because the data have not been seasonally adjusted.
Important components are components with a large spectral density, and, thus,
the estimated damping parameter specifies how tightly the important
components are distributed around the estimated central frequency. We
calculate and plot the spectral density implied by these parameter estimates
. psdensity omega density
. twoway line omega density
Moving on to prediction, we predict the trend and the seasonal components:
. predict strend, trend
. predict season, seasonal
Below we graph the trend component in the top panel and the seasonal
component in the bottom panel.
We can also forecast the median unemployment duration and graph the results.
. tsappend, add(12)
. predict duration_f, dynamic(tm(2009m1)) rmse(rmse)
For a complete list of what’s new in time-series analysis,
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New in Stata 12
for more about what was added in Stata Release 12.