(This article was originally published at No Hesitations, and syndicated at StatsBlogs.)
Note that you can use the same idea in time-series contexts. Even in a pure time series, you can allow for period-by-period time effects, broken polynomial trend with an arbitrary number of breakpoints, etc., via regularization. It turns out that a fascinating small literature on so-called "indicator saturation estimation" pursues this idea. The "indicators" are things like period-by-period time dummies, break-date location dummies, etc., and "saturation" refers to the profligate parameterization. Prominent contributors include David Hendry and Soren Johanssen; see this new paper and those that it cites. (Very cool application, by the way, to detecting historical volcanic eruptions.)
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