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We study the problem of nonparametric estimation of the fractional derivativeof unknown spectral function of Gaussian stationary sequence (time series) andshow that these problems is well posed with the classical speed of convergencewhen the order of derivative is less than 0.5. We prove also the asymptoticalunbiaseness and normality of offered estimates with optimal speed ofconvergence. For the construction of the confidence region in some functionalnorm we establish the Central Limit Theorem in correspondent space ofcontinuous functions for offered estimates.

Problem of Estimation of Fractional Derivative for a Spectral Function of Gaussian Stationary Processes