I'm pleased to report that my latest advances in the domain of `regularization' (see 1) - my experiments on `regularization supports customization' - are exciting. In a nutshell:
- Regularization will be accessible to users of the `new' I-MDFA in terms of: smoothness, rate of decay and cross-sectional flexibility (all features address `filter parameters')
- I call this a proper regularization troika.
- It (the troika) allows to address very richly (possibly infinitely) parameterized filter designs: large lag-orders and/or high-dimensional multivariate designs are OK!
- Ignoring regularization replicates the 2011-vintage of I-MDFA: all you did with my R-code up to yet could be replicated perfectly. But you could do more...
- The user of the new procedure is invited to specify how much overfitting he is willing to accept... (strange invitation, isn't it?)
- For the `seemingly clever' user: specifying `zero-overfitting' is not meaningful since the solution will be a `zero-filter'... so you have to take some meaningful decision in terms of a tradeoff!
- Given this user disponibility (amount of overfitting), the new procedure will search for `optimal' regularization in a hyper-space of the aforementioned regularization-troika.
- The hyper-space is entirely specified by the `amount of overfitting' the user is willing to endure.
- I-MDFA solutions are constrained to lie in the hyperspace defined by the `amount of overfitting'.
- Unfortunately I don't have closed-form solutions... And I don't expect to have any soon!
- And numerical computations are laborious...
- But the added value could be substantial!
- For those users who don't know how much overfitting they would like to endure I'm proposing kind of a generalized information criterion which assists in finding the `optimal amount of overfitting'.
- The proposed statistic has nothing substantial in common with `information criteria'.
- But it looks and feels alike.
There is a lot of work/investigation/tweaking to do now. But it feels good!
Stay tuned and enjoy 2012!