ABSTRACT
For a stationary process with spectral density f(>..), Taniguchi (1987) discussed fitting a parametric spectral model fe(>..) by a criterion D(f0J) which measures the nearness of fo to f. Then a new estimator (j of () was proposed by the value minimizing D(f0 ,i,,) with respect to (), where!,, is a suitable non parametric spectral estimator off based on n observed stretch. Under appropriate conditions it was shown that the main order term of y'/1(0-())can be written as F = y'/1 J:rr 1j!{>..){/,,(>..) -/(>..)} d>.. where 1/J(>..) is an integrable function. Although nonparametric spectral estimators deviate from f(>..) by a larger probability order than n-1/ 2, Taniguchi (1987) showed that the integral functionals obey the y'/1 -consistent asymptotics, and that (j is asymptotically efficient iff = .f0• Thus we can see that the integral functional F is the key quantity. Hence, the purpose of this paper is to develop various statistical analyses based on integral functionals of spectral densities.
