Parameter Estimation and Hypothesis Testing in Spectral Analysis of Stationary Time Series

. . ) (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