Abstract :
Slowly varying ~SV! regressors arise commonly in empirical econometric work,
particularly in the form of semilogarithmic regression and log periodogram regression+
These regressors are asymptotically collinear+ Usual regression formulas for
asymptotic standard errors are shown to remain valid, but rates of convergence
are affected and the limit distribution of the regression coefficients is shown to be
one dimensional+ Some asymptotic representations of partial sums of SV functions
and central limit theorems with SV weights are given that assist in the development
of a regression theory+ Multivariate regression and polynomial regression
with SV functions are considered and shown to be equivalent, up to standardization,
to regression on a polynomial in a logarithmic trend+ The theory involves
second-, third-, and higher-order forms of slow variation+ Some applications to
the asymptotic theory of nonlinear trend regression are explored+
