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

Zusatztext

. ) (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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