The Predictive Space, or, If x predicts y, what does y tell us about x?

Donald Robertson and Stephen Wright

No 1210, Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics

Abstract: A predictive regression for y(t) and a time series representation of the predictors, x(t), together imply a univariate reduced form for y(t). In this paper we work backwards, and ask: if we observe y(t), what do its univariate properties tell us about any x(t) in the "predictive space" consistent with those properties? We provide a mathematical characterisation of the predictive space and certain of its derived properties. We derive both a lower and an upper bound for the R^2 for any predictive regression for y(t). We also show that for some empirically relevant univariate properties of y(t), the entire predictive space can be very tightly constrained. We illustrate using Stock and Watson's (2007) univariate representation of inflation.

Date: 2012-04
New Economics Papers: this item is included in nep-for
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://eprints.bbk.ac.uk/id/eprint/5949 First version, 2012 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bbk:bbkefp:1210

Ordering information: This working paper can be ordered from

Access Statistics for this paper

More papers in Birkbeck Working Papers in Economics and Finance from Birkbeck, Department of Economics, Mathematics & Statistics Malet Street, London WC1E 7HX, UK.
Bibliographic data for series maintained by ( this e-mail address is bad, please contact ).