Robertson, D. and Wright, Stephen (2012) The predictive space or if x predicts y, what does y tell us about x? Working Paper. Birkbeck College, University of London, London, UK.
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Abstract
A predictive regression for yt and a time series representation of the predictors, xt, together imply a univariate reduced form for yt. In this paper we work backwards, and ask: if we observe yt, what do its univariate properties tell us about any xt 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 R2 for any predictive regression for yt. We also show that for some empirically relevant univariate properties of yt, the entire predictive space can be very tightly constrained. We illustrate using Stock and Watson's (2007) univariate representation of inflation.
Metadata
| Item Type: | Monograph (Working Paper) |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Business and Law > Birkbeck Business School |
| Research Centres and Institutes: | Applied Macroeconomics, Birkbeck Centre for |
| Depositing User: | Administrator |
| Date Deposited: | 11 Jan 2013 11:47 |
| Last Modified: | 02 Aug 2023 17:01 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/5949 |
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