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I have to build a classification model to predict recessions. I have selected a set of features (some are economic and some are financial). I have noticed that it is good pratice often to add to the original features also their lagged versions. So basically the features are lagged/shifted forward in the "future" of 1 or more samples. It seems that shifting in the future features samples have some predictive power. See picture below as an example

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Can anybody please provide me with an econometric justification of this?

Thanks Luigi

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    $\begingroup$ I’m voting to close this question because the question is not related to quantitative finance. It might better fit on Economics Stack Exchange or Cross Validated. $\endgroup$ Jan 8 at 16:37
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    $\begingroup$ Maybe better there, but is your definition of "quantitative finance" so tight that questions of a quantitative nature related to finance fall outside of scope? Anything that does not require set/measure theory, differential back-propagation of errors, and Ito's Lemma for is for idiots that don't belong here? I vote answer the question. I just did. Let's see if the OP is happy. $\endgroup$
    – demully
    Jan 10 at 23:06
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    $\begingroup$ ps "econometrics" is specifically listed as being in-scope, just saying. $\endgroup$
    – demully
    Jan 12 at 8:47
  • $\begingroup$ @demully, I totally agree, this is a question on factor models in the end, which is one of the most popular and oldest problem in econometrics. I feel it is pretty unfair that someone else closes the question just because he/she thinks is not the right fit for this forum.. $\endgroup$
    – Luigi87
    Jan 12 at 9:11
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In its simplest terms, imagine you were just using the yield curve as your single predictor of recessions. Suppose (horribly simplistically) that curve inversions tend to signal downturns in 12-18 months time. The curve 12-18 months ago is thus a relevant variable for whether the economy is going into recession or not today.

It might also be the case that the curve today tends to have started to steepen back up at the point at which the economy starts to shrink. So it might even be the case that the current value of the curve would not then itself be relevant.

These kind of effects are classically represented in traditional econometrics as the "partial adjustment model", or as the "adaptive expectations model". The two are grounded in different, almost completely opposed, theoretical/philosophical assumptions. The former assume (and try to distinguish between) the longer-term versus shorter-term effect of your regressors on your response variable. The latter assume that your regressors already embed some (unknown) anticipation about the future of your response, and so the behaviour of your response also has to reflect revisions to these expectations, when the actual outcomes in your regressors play out differently to the (unknown) expected ones.

As such, the two models appear very different at first. However, there is a big irony here. You end up with the same final structure modelling either via regression, namely:

Y = a.X + b.laggedX + e

hope this helps, DEM

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