SEF-Blog: Signal Extraction and Forecasting

I go on with my `replication'-strategy consisting in `step-by-step' - tutorial style - calibrations of I-MDFA on classical filters and/or model-based approaches: 

• Replication of HP was proposed in 1
• Replication of TRAMO/SEATS was proposed in 2 , see section 6 in the posted paper (R-code will be posted here soon).

This entry is about Replication of the CF-filter (R-code, plots and discussions are provided below). As for the HP-filter, this entry was initiated by a SEFBlog-reader: thanks for inputs and feedbacks!

Here's the latest paper written with my colleague Tucker McElroy from Census Bureau: Trilemma.pdf. It conveys a new perspective on forecasting/signal-extraction by breaking-up a  fundamental uncertainty-principle. Specifically, we propose to go beyond the traditional dichotomic view (bias-variance dilemma) by decomposing the mean-square norm into three competing terms - Trilemma - which allow to `customize' forecasting models and/or signal extraction filters according to specific research priorities. This should sound familiar to regular SEFBlog readers...  We apply the Sweave-package so that results in the article can be replicated (R-code will be posted in a subsequent entry).

The problem evoked at the end of my previous entry 1 (dedicated to the replication of the HP-filter by I-MDFA) has been addressed. Specifically the new (R-) code release I-MDFA_new.r allows to apply the i2-constraint (vanishing-time shift) to arbitrary Lag specifications. Since the relevant issues are more subtle than simple `bug-tracking' I revised my companion paper too, see section 8. I'd like to thank explicitly/expressively SEFBlog readers for reporting problems/bugs and for suggesting directions for future developments!

I suggested in various places on this Blog that I-MDFA is able to replicate traditional model-based approaches and/or classical `ad hoc' filters. The following tutorial illustrates a replication of the (practically relevant real-time) HP-filter by I-MDFA. I shaped this entry into the form of a short tutorial, providing (R-) code and graphs. It should be clear that once a particular filter has been replicated by I-MDFA, the whole customization and the new regularization apparatus can be applied in order to match particular research priorities. Therefore the scope of this entry is potentially more general than suggested by its title.

• Replication and customization of the model-based approach is proposed in a new working paper by McElroy and Wildi (2012) (still under revision). I'll poste code and paper in Summer this year.

April 27:

• the McElroy/Wildi (2012) paper is posted in 1.
• A replication of the CF-filter is provided in 2.

I'm pleased to inform that the EURI has its own dedicated website. The indicator tracks Euro-Area (EA) GDP based on DG-ECFIN data. The published design hasn't passed all consistency checks, yet, any may be subject to slight revisions in the up-coming months. Let me just highlight that the fast indicator anticipated the upturn in the EA in October 2011; it is now in the positive zone. I proposed the EURI as an illustration of the new Regularization Troïka (section 7 in my up-dated companion paper 1), see the corresponding links on the dedicated  EURI-site. The underlying R-code has been discussed in my live-tutorial round 2 (you may check the category `tutorial' on the left margin): we shall publish the code on the EURI-site too.

I'm here proposing a (long awaited - by me -) comprehensive revision of my companion I-MDFA paper posted in 1, some time ago. I derive closed-form solutions for mean-square, customized, regularized and/or constrained I-MDFA designs based on appealing `linear-regression' expressions. I conjecture that this new approach should be appealing - more than my previous attempts - to potentially interested users. In particular regularization (my funky `Regularization Troika') is treated in full detail. And the ominous i1-constraint is treated in full complexity/generality. I took opportunity to upgrade the original title too: enjoy elements.pdf. R-code is posted in 2 (you might want to check for regular up-dates).

• April 03: The following revised version covers also the cases i1<-T, i2<-F  and i1<-F, i2<-T in section 7: elements_03042012.pdf
• April 06: a new section 6 (inference) has been added and revised and formulas in sections 8 and 9 are corrected: elements_06042012.pdf 
  • My desire to address inference in a few lines was futile and I had to resign: reference to the literature is given instead... These things are too complex and need extensive developments: there are 8-th order moments of the data involved! I remember how painful the derivation of results (theorem 10.20 in 2008-book) were at that time and I don't want to discredit my 2008-efforts by publishing some easy-going `dirt' 4 years later (my shame dictated that I removed an earlier revision of this paper: note however that my errors were quite instructive and maybe I'll post this earlier `dirty' version again, with some comments of the kind `what's wrong here').  
• April 19: after a feedback by a SEFBlog-user I revised my code (see 2) as well as section 8 in my companion paper elements_19042012.pdf. Context is provided in 3.

I'm currently working on several projects/publications that might be of interest to SEFBlog-readers:

• EURI: we're getting close to launch the new real-time indicator for the Euro-Area on a dedicated website.
• A new working paper in collaboration with Tucker McElroy will be available soon here. A novelty of this paper will be that Latex-code and R-code will be joined in a single R-file (so called rnw-file). Thus readers of the paper can replicate graphs and tables by following/debugging my R-code: readers become users. I conjecture that some SEFBlog-veterans will like this article.
• I'm working on a leading-indicator project for G7 member countries. Depending on project partner's feedback I'll be able to poste results here. The whole report is based on mixing Latex-code and R-code i.e. replication of results (tables/graphs) is a breeze.

Soon to be seen here.