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. . ) (under the assumption that the spectral density exists). For
this reason, a vast amount of periodical and monographic literature
is devoted to the nonparametric statistical problem of estimating
the function tJ( T) and especially that of leA) (see, for example,
the books [4,21,22,26,56,77,137,139,140,]). However, the empirical
value t;; of the spectral density I obtained by applying a certain
statistical procedure to the observed values of the variables Xl' .
. . , X , usually depends in n a complicated manner on the cyclic
frequency). . This fact often presents difficulties in applying the
obtained estimate t;; of the function I to the solution of specific
problems rela ted to the process X . Theref ore, in practice, the t
obtained values of the estimator t;; (or an estimator of the
covariance function tJ~( T" are almost always "smoothed," i. e. ,
are approximated by values of a certain sufficiently simple
function 1 = 1
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