Two earlier regularization posts focused on panel data and generic time series contexts. Now consider a specific time-series context: long memory. For exposition consider the simplest case of a pure long memory DGP, (1−L)dyt=εt with |d|<1/2. This ARFIMA(0,d,0) process is is AR(∞) with very slowly decaying coefficients due to the long memory. If you KNEW the world was was ARFIMA(0,d,0) you'd just fit d using GPH or Whittle or whatever, but you're not sure, so you'd like to stay flexible and fit a very long AR (an AR(100), say). But such a profligate parameterization is infeasible or at least very wasteful. A solution is to fit the AR(100) but regularize by estimating with ridge or a LASSO variant, say.
Related, recall the Corsi "HAR" approximation to long memory. It's just a long autoregression subject to coefficient restrictions. So you could do a LASSO estimation, as in Audrino and Knaus (2013). Related analysis and references are in a Humboldt University 2015 master's thesis.)
Finally, note that in all of the above it might be desirable to change the LASSO centering point for shrinage/selection to match the long-memory restriction. (In standard LASSO it's just 0.)
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