IDEAS home Printed from https://ideas.repec.org/p/bbk/bbkefp/1210.html
   My bibliography  Save this paper

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

Author

Listed:
  • Donald Robertson

    (University of Cambridge)

  • Stephen Wright

    (Department of Economics, Mathematics & Statistics, Birkbeck)

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.

Suggested Citation

  • Donald Robertson & Stephen Wright, 2012. "The Predictive Space, or, If x predicts y, what does y tell us about x?," Birkbeck Working Papers in Economics and Finance 1210, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:1210
    as

    Download full text from publisher

    File URL: http://www.bbk.ac.uk/ems/research/wp/2012/PDFs/BWPEF1210.pdf
    File Function: First version, 2012
    Download Restriction: no

    References listed on IDEAS

    as
    1. John Y. Campbell & N. Gregory Mankiw, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 857-880.
    2. Marc P. Giannoni & Jean Boivin, 2005. "DSGE Models in a Data-Rich Environment," Computing in Economics and Finance 2005 431, Society for Computational Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Monticini, Andrea & Ravazzolo, Francesco, 2014. "Forecasting the intraday market price of money," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 304-315.
    2. repec:ctc:serie1:def10 is not listed on IDEAS

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bbk:bbkefp:1210. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: http://www.ems.bbk.ac.uk/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.