VTeX: Solutions for Science Publishing logo


  • List of journals
  • Browse subjects
  • About Publisher
  • Help
  • Sitemap
Login Register

  1. Home
  2. Journals
  3. MSTA
  4. Issues
  5. Volume 1, Issue 2 (2014)
  6. Asymptotics for functionals of powers of ...

Modern Stochastics: Theory and Applications*

Submit your article Information Become a Peer-reviewer VTeX
  • Article info
  • Full article
  • Related articles
  • More
    Article info Full article Related articles

Asymptotics for functionals of powers of a periodogram
Volume 1, Issue 2 (2014), pp. 181–194
Lyudmyla Sakhno  

Authors

 
Placeholder
https://doi.org/10.15559/15-MSTA15
Pub. online: 4 February 2015      Type: Research Article      Open accessOpen Access

Received
22 November 2014
Accepted
8 January 2015
Published
4 February 2015

Abstract

We present large sample properties and conditions for asymptotic normality of linear functionals of powers of the periodogram constructed with the use of tapered data.

References

[1] 
Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Statistical inference based on the information of the second and third order. J. Stat. Plan. Inference 137, 1302–1331 (2007) MR2301481. doi:10.1016/j.jspi.2006.03.001
[2] 
Anh, V.V., Leonenko, N.N., Sakhno, L.M.: Evaluation of bias in higher-order spectral estimation. Teor. Imovir. Mat. Stat. 80, 1–14 (2009); English edition: Theory Probab. Math. Stat. 80, 1–14 (2010) MR2541947
[3] 
Avram, F., Leonenko, N., Sakhno, L. On the generalized Szegö theorem, Hölder-Young-Brascamp-Lieb Inequality and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM Probab. Stat. 14, 210–255 (2010) MR2741966. doi:10.1051/ps:2008031
[4] 
Avram, F., Leonenko, N., Sakhno, L.: Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities. Stoch. Process. Appl. (2015) doi:10.1016/j.spa.2014.11.010
[5] 
Bentkus, R.: Cumulants of estimates of the spectrum of a stationary sequence. Liet. Mat. Rink. 16, 37–61 (1976) (in Russian); English translation: Lith. Math. J. 16, 501–518 (1976) MR0431571
[6] 
Chiu, S.: Weighted least squares estimators on the frequency domain for the parameters of a time series. Ann. Stat. 16, 1315–1326 (1988) MR0959204. doi:10.1214/aos/1176350963
[7] 
Dahlhaus, R.: Spectral analysis with tapered data. J. Time Ser. Anal. 4, 163–175 (1983) MR0732895. doi:10.1111/j.1467-9892.1983.tb00366.x
[8] 
Deo, R.S., Chen, W.W.: On the integral of the squared periodogram. Stoch. Process. Appl. 85, 159–176 (2000) MR1730613. doi:10.1016/S0304-4149(99)00071-X
[9] 
Leonenko, N.N., Sakhno, L.M.: On the Whittle estimators for some classes of continuous parameter random processes and fields. Stat. Probab. Lett. 76, 781–795 (2006) MR2266092. doi:10.1016/j.spl.2005.10.010
[10] 
Leonov, V.V., Shiryaev, A.N.: On a method of calculation of semi-invariants. Theory Probab. Appl. 4, 319–329 (1959) MR0123345
[11] 
McElroy, T., Holland, S.: A local spectral approach for assessing time series model misspecification. J. Multivar. Anal. 100, 604–621 (2009) MR2478185. doi:10.1016/j.jmva.2008.06.010
[12] 
Sakhno, L.: Minimum contrast estimation of stationary processes based on the squared periodogram. Lith. Math. J. 52, 400–419 (2012) MR3001040. doi:10.1007/s10986-012-9183-3
[13] 
Taniguchi, M.: On estimation of the integrals of certain functions of spectral density. J. Appl. Probab. 17, 73–83 (1980) MR0557436

Full article Related articles PDF XML
Full article Related articles PDF XML

Copyright
© 2014 The Author(s). Published by VTeX
by logo by logo
Open access article under the CC BY license.

Keywords
Asymptotic normality periodogram tapered data

MSC2010
60F05 62M15 60G10

Metrics
since February 2017
0

Article info
views

0

Full article
views

4

PDF
downloads

3

XML
downloads

Export citation

Copy and paste formatted citation
Placeholder

Download citation in file


Share


RSS

  • About Publisher
Powered by PubliMill  •  Privacy policy