ABSTRACT
This chapter discusses the interplay between the design matrix X, long memory in the errors, and the distribution of regression estimates. A more general aproach to characterizing the limiting behavior of slope estimates in regression is to consider the so-called regression spectrum. If zero is an element of the regression spectrum, then it is more difficult to separate the process ϵt from the effect of the explanatory variables. A typical example is a polynomial trend. In contrast, the regression spectrum of a seasonal or harmonic component, as defined in the above examples, does not include zero. If the regression spectrum contains non-zero frequencies only, one obtains the same result as for spectral densities which are continuous in the whole interval. If zero is an element of the regression spectrum, then the pole of the spectral density changes the efficiency of the least squares estimator.
