Signal Extraction and Forecasting

Something about customization...

The intuitive simplicity of the classic model-based approach discussed in  (1) distracts from a deeply-rooted problem: an implicit assumption which does not hold, in practice, and whose undesirable effects are magnified in signal extraction, in particular. I here introduce and briefly discuss the 'broken link'.

In (1) I argued: "-- as a by-product -- performances (MSE-contributions by the time-shift) are implicitly emphasized at the practically relevant turning-points (the extrema) of the original series. In many applications, these are the time-points towards which a decision-maker is supposed to (well...) make a decision...", see (1) for the simple geometric argument. Isn't that feature, namely the implicit emphasis of turning points, both desirable and intriguing? 

This entry is about the last piece of R-code in MDFA_Legacy_MSE.r . I'm showing how to implement a bivariate real-time ( concurrent ) filter in the MDFA-package and I'm analyzing various leading indicator designs (various combinations of lead and noise parameters). The whole material is copy-paste from  MDFA , chapter 4 which highlights plain vanilla mean-square error (MSE-) performances.

Here's a very simple and short example illustrating replication of  (the univariate) DFA-MSE criterion by the multivariate MSE-wrapper as well as by the generic multivariate MDFA-function of the MDFA-package (consistency check). The example briefly goes over the parametrization of MDFA-functions (discussed in step-by-step introduction ). Sample code relies on MDFA_Legacy_MSE.r   (see  MDFA tutorial for installation).

In the previous blog-post (1) I introduced some formal arguments justifying the DFA-MSE criterion. Here I'd like to provide some intuitive background. I'll introduce transfer functions, amplitude functions and time-shift functions. Moreover, I'll introduce concepts and ideas preparing for the ATS-trilemma (customization). Sample (R-) code will be based on MDFA_Legacy_MSE.r posted earlier, see  MSE-tutorial .

In the previous blog-post  (1) I specified the generic target in signal extraction and forecasting. I now present and discuss the corresponding (MSE) optimization criterion , see  Optimal Real-Time Filters for Linear Prediction Problems for background. The exposition address es technical issues which will be illustrated by sample (R-) code ( MDFA_Legacy_MSE.r posted earlier, see  MSE-tutorial ). An intuitive interpretation of the criterion is provided in the follow-up post.

I here briefly specify the concept of a ' target signal ' and I introduce so-called ' ideal ' (symmetric) filters. Illustrations are based on the sample MSE R-code MDFA_Legacy_MSE.r posted earlier, see  MSE-tutorial .

The tutorial proposed in 1 replicated chapters 1-4 in MDFA . I'd like to briefly review the various functions available in the MDFA-package and discuss their handling (parametrization, data-feed).

The predicate ' direct ' refers to the fact that the optimization criterion emphasizes 'directly' filter performances (instead of classic one-step ahead mean-square error performances prevalent in maximum likelihood approaches). The term ' filter ' refers to the fact that the outcome of the optimization is not a model , but a filter instead. The formal mathematical background (in a mean-square error perspective) is provided in Optimal Real-Time Filters for Linear Prediction Problems .

I here provide a tutorial on univariate as well as on multivariate real-time filtering, using the MDFA-package on Github.  I will emphasize the Mean-Square Error ( MSE ) norm 'only' in this tutorial. The material is designed as an entry-point to the MDFA-methodology (see Advances in Signal Extraction and Forecasting ) and to the R-package.

The so-called Multivariate Direct Filter Approach, MDFA, is my workhorse for all recent and current (and likely future) research projects in the context of economic (macro/finance) SEF (signal extraction and forecasting) applications. One can access the MDFA-package on Github.

It's been a while since I posted on the topic... This blog is the new site -- the new home for MDFA and related topics -- where I will regularly publish/share  documents, notes, publications, insights, experience, R-code on 'Signal Extraction and Forecasting' (SEF in short).