SOME LIMIT-THEOREMS FOR PARTIAL SUMS OF QUADRATIC-FORMS IN STATIONARY GAUSSIAN VARIABLES

Limit theorems with a non-Gaussian limiting distribution have been obtained, under appropriate conditions for partial sums of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence by a number of people. The normalization has typically been nα, with 1/2<α<1 where n is the sample size. Here examples of limit theorems are given for quadratic functions with long range memory (not instantaneous) with a normalization nα, 0<α<1/2. © 1979 Springer-Verlag.