The authors consider the stationary linear processes in the form
with a noise sequence of i.i.d. random variables which may have finite or infinite variance. The model may exhibit long-range dependence. The integrated periodogram can be interpreted as the relative error of the empirical spectral density compared with the true spectral density in the interval . The authors derive functional limit theorems for the randomly centered sequence
The results are applied to obtain corresponding Kolmogorov–Smirnov and Cramér–von Mises goodness-of-fit tests.