SPECTRAL ESTIMATION FOR STRONGLY DEPENDENT STATIONARY GAUSSIAN-PROCESSES

The empirical periodogram of a strongly dependent stationary gaussian processes with EX(o)X(k) almost-equal-to c\k\-alpha (alpha < 1/2) satisfies for any (1/2 + epsilon)-Holder continuous function g, if g(O) not-equal O then n-alpha(I(n) (g) - EI(n)(g)) --> L g (O) Y, Y for some non gaussian random variable Y and if fg is continuous square-root n(I(n)(g) - EI(n)(g)) --> L N(0, 4 pi-integral-pi f2 (x) g2 (x) dx). The spectral density f of the process is assumed to be continuous out of the origin. Considering a sequence (g(n,x)) leads to estimates of f at a point x with analogous properties.