K. Dzhaparidze 
Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series [PDF ebook] 

. . ) (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 t J( T) and especially that of le A) (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 t J~( T are almost always "smoothed, " i. e. , are approximated by values of a certain sufficiently simple function 1 = 1