Law of Iterated Logarithm for Weighted Sums of Functionals of Long-Memory Gaussian Sequences

We prove iterated-logarithm results for weighted nonlinear functionals of long-memory stationary Gaussian sequences with regularly varying weights. The leading Hermite chaos determines the natural almost-sure scale. In the linear case we obtain the sharp variance-normalized LIL constant. In the nonlinear fixed-chaos regime we identify the weighted functional cluster set and obtain a variational formula for the nonlinear LIL constant.