Periodogram Estimator Properties of the Parameters of the Regression Model with Strongly Dependent Noise

The problem of detection of hidden periodicities is considered in the paper. In the capacity of useful signal model the harmonic oscillation observed on the background of random noise, that is a local functional of Gaussian strongly dependent stationary process is taken. For estimation of unknown angular frequency and amplitude of harmonic oscillation periodogram estimator is chosen, for which sufficient conditions of asymptotic normality are obtained and limit normal distribution is found. To obtain the main result there were used limit theorems of random processes, weak convergence of a family of measures to the spectral measure of a regression function, etc. The novelty, compared with the known results in the theory of periodogram estimator in observation models on weakly dependent noise, is assuming that the random noise is a local functional of Gaussian strongly dependent stationary process.

Publication year: 
С. 59—65. Бібіогр.: 17 назв.

1. Серебренников М.Г., Первозванский А.А. Выявление скрытых периодичностей. — М.: Наука, 1965. — 244 c.
2. P. Whittle, “The simultaneous estimation of a time series harmonic components and covariance structure”, Trabajos Estadistica, vol. 3, pp. 43—57, 1952.
3. A.M. Walker, “On the estimation of a harmonic component in a time series with stationary dependent residuals”, Adv. in Appl. Probability, vol. 5, pp. 217—241, 1973.
4. E.J. Hannan, “The estimation of frequency”, J. Appl. Probability, vol. 10, pp. 510—519, 1973.
5. A.V. Ivanov, “A solution of the problem of detecting hidden periodicities”, Theor. Probability and Math. Statist., no. 20, pp. 51—68, 1980.
6. Кнопов П.С. Оптимальные оценки параметров стохастических систем. — К.: Наук. думка, 1981. — 152 с.
7. Гречка Г.П., Дороговцев А.Я. Об асимптотических свойствах периодограмной оценки частоты и амплитуды гармонического колебания // Вычисл. и прикл. математика. — 1976. — Вып. 28. — С. 18—31.
8. S. Chatterjee and V.C. Vani, “An Extended Matched Filtering Methods to Detect Periodicities in a Rough Grating for Extremely Large Roughness”, Bull. of the Astronomical Society of India, vol. 31, pp. 457—459, 2003.
9. A.V. Levenets et al., “Estimating signal spectra with a method of determining concealed periodicities in zero crossings”, Measurement Techniques, vol. 39, no. 9, pp. 909—913, 1996.
10. S. Chatterjee and V.C. Vani, “Scattering of light by a periodic structure in the presence of randomness. V. Detection of successive peaks in a periodic structure”, Appl. Optics, vol. 45, pp. 8939—8944, 2006.
11. M. Hinich, “Detecting a hidden periodic signal when its period is unknown, Acoustics”, Speech and Signal Proc., vol. 30, is. 5, pp. 747—750, 1982.
12. I. Iavorskyj and V. Mykhajlyshyn, “Detecting hidden periodicity of time-series generated by nonlinear processes in magneto-plasma”, in Proc. 6th Int. Conf. on Volume “Mathematical methods in Electromagnetic Theory”, is. 10-13, 1996, pp. 397—400.
13. H. Arsham, “A test sensitive to extreme hidden periodicities”, Stochastic Environmental Research and Risk Assessment, vol. 11, no. 4, pp. 323—330, 1997.
14. J. Malisic et al., “Application of some statistical tests for hidden periodicity in the Serbian annual precipitation sums”, Hungarian Meteorological Service, vol. 103, no. 4, pp. 237—247, 1999.
15. Жураковський Б.М., Іванов О.В. Консистентність оцінки найменших квадратів параметрів суми гармонічних коливань у моделях із сильнозалежним шумом // Наукові вісті НТУУ “КПІ”. — 2010. — № 4. — С. 60—66.
16. Жураковський Б.М. Відшукання прихованих періодичностей у моделі із сильнозалежним випадковим шумом: Дипл. робота: 01.01.05; НТУУ “КПІ”. — К., 2010. — 74 с.
17. B.G. Quinn and E.J. Hannan, The Estimation and Tracking of Frequency. New York: Cambridge University Press, 2001.

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