A restriction on a semiparametric or nonparametric econometric time series model determines the value of a finite-dimensional functional τ of an infinite-dimensional nuisance function. The estimate of τ and its estimated covariance matrix use nonparametric probability and spectral density estimation. A consequent test of the restriction is given approximate large sample justification under absolute regularity on the time series and other conditions. The methodology relates closely to recent proposals of Powell, Stock, Stoker and Robinson in cross-sectional applications, but serial dependence generally affects the test statistic's form, as well as statistical theory.

We propose a specific characteristics framework in order to construct linkages between alternative conceptual approaches to modelling product differentiation. First, it is shown that a demand system which satisfies the gross substitutes property imposes specific requirements on the locations of products. In particular, the dimension of the characteristics space must be larger than or equal to the number of products minus one. We then identify a method for casting a given demand system (subject to certain restrictions) into our characteristics framework. This is illustrated for the logit, probit and linear probability models of discrete choice theory. Finally, we find a characteristics representation of the CES representative consumer.