Variogram analysis of stochastic processes

Authors

  • Tatsiana V. Tsekhavaya Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

Keywords:

stochastic process, intrinsic stationarity, semivariogram, confidence interval

Abstract

Properties of the semivariogram of an intrinsically stationary continuous-time random process with finite second moment are investigated. A necessary and sufficient conditions for a continuous function to be semivariogram are found. Confidence intervals for the semivariogram of Gaussian stationary stochastic process are defined. Properties of ꭓ2-distribution are used for constructing confidence intervals for semivariogram. The proposed confidence intervals are more informative compared with point estimates of the semivariogram. 

Author Biography

  • Tatsiana V. Tsekhavaya, Belarusian State University, Niezaliežnasci Avenue, 4, 220030, Minsk, Belarus

    PhD (physics and mathematics), docent; associate professor at the department of probability theory and mathematical statistics, faculty of applied mathematics and com puter sciences

References

  1. Tsekhavaya Т. V. [The properties of the variogram of intrinsically stationary random processes]. Teoriya veroyatnostei, matematicheskaya statistika i ikh prilozheniya : proc. Int. sci. of conf. (Minsk, 22 April, 2004). Мinsk, 2004. P. 181–186 (in Russ.).
  2. Tsekhavaya Т. V. Asymptotic distribution of the semivariogram estimator of Gaussian stochastic process. Vestnik BGU. Ser. 1, Fizika. Matematika. Informatika. 2015. No. 1. Р. 89 – 95 (in Russ.).
  3. Tsekhavaya T. V. Properties of the intrinsically stationary stochastic processes. J. Belarus. State Univ. Math. Inform. 2017. No. 1. P. 28–33 (in Russ.).
  4. Shiryaev А. N. [Probability]. Мoscow, 1989 (in Russ.).
  5. Djenkins G., Vatts D. [Spectral analysis and its applications] : in 2 vol. Мoscow. 1971. Vol. 1 (in Russ.).
  6. Lloyd E., Lederman Yu. (eds). Spravochnik po prikladnoy statistike [Handbook of applicable mathematics] : in 2 vol. Moscow, 1989. Vol. 1: Finansy i statistika (in Russ.).

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Published

2018-01-24

Issue

No. 2 (2017): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
Tsekhavaya, T.V. 2018. Variogram analysis of stochastic processes. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jan. 2018), 23–27.