Construction of estimates of spectral densities with a given accuracy over intersecting intervals of observations
Abstract
The article proposes a new method for determining the number of splitting intervals and the number of observations in them when building estimates of the spectral densities of stationary random processes with a given accuracy over intersecting observation intervals based on asymptotic results, obtained for the first moment of convergence rate under the assumption that the spectral density satisfies the Lipschitz condition. Two cases are considered: with a single and arbitrary data taper. As a result, an algorithm is proposed for constructing estimates for intersecting intervals of observations with a given accuracy. This algorithm was tested on model examples for random AR(4) processes, using data taper of Riesz, Bochner, Parzen. The proposed method will be useful to the researcher in analyzing data in the form of stationary random processes using nonparametric methods of spectral analysis in an automated mode.
References
- Surmach AI, Semenchuk NV. [Methods of data analysis using consistent spectral density estimates]. In: Teoriya veroyatnostei, sluchainye protsessy, matematicheskaya statistika i prilozheniya. Sbornik nauchnykh statei mezhdunarodnoi konferentsii, posvyashchennoi 80-letiyu professora, doktora fiziko-matematicheskikh nauk G. A. Medvedeva; 23–26 fevralya 2015 g.; Minsk, Belarus’ [Probability theory, random processes, mathematical statistics and applications. Proceedings of the International conference in honor of 80 years jubilee of professor, doctor of physical and mathematical sciences Gennady Medvedev; 2015 February 23–26; Minsk, Belarus]. Minsk: Respublikanskii institut vysshei shkoly; 2015. p. 305–310. Russian.
- Brillindzher D. Vremennye ryady. Obrabotka dannykh i teoriya [Time series. Data processing and theory]. Moscow: Mir; 1980. 536 p. Russian.
- Troush NN. Asimptoticheskie metody statisticheskogo analiza vremennykh ryadov [Asymptotic methods of statistical analysis of time series]. Minsk: Belarusian State University; 1999. 218 p. Russian.
- Semenchuk NV, Troush NN. The comparative analysis of some periodogram’s estimates of spectral density. Trudy Instituta matematiki. 2007;15(2):90 –103. Russian.
- Semenchuk NV. [About choosing the optimal data taper]. Vesnik Grodzenskaga dzjarzhawnaga wniversiteta imja Janki Kupaly. Seryja 2. Matjematyka. Fizika. Infarmatyka, vylichal’naja tjehnika i kiravanne. 2012;2(129):61– 66. Russian.
- Zhurbenko IG. Spektral’nyi analiz vremennykh ryadov [Spectral analysis of time series]. Moscow: Moscow State University; 1982. 168 p. Russian.
- Alekseev VG. [On the calculation of the spectra of stationary random processes for samples of large volume]. Problemy peredachi informatsii. 1980;16(1):42– 49. Russian.
- Alekseev VG. [Estimates of the spectral densities of some models of stationary random processes]. Problemy peredachi informatsii. 1985;21(2):42– 49. Russian.
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