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
