Title

Effective Number of Observations and Unbiased Estimators of Variance for Autocorrelated Data - an Overview

Journal title

Metrology and Measurement Systems

Yearbook

2010

Issue

No 1

Authors

Zięba, Andrzej

Keywords

autocorrelated ; time series ; estimator ; unbiased ; variance ; effective number of observations

Divisions of PAS

Nauki Techniczne

Publisher

Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation

Date

2010

Type

Artykuły / Articles

Identifier

DOI: 10.2478/v10178-010-0001-0 ; ISSN 2080-9050, e-ISSN 2300-1941

Source

Metrology and Measurement Systems; 2010; No 1

Pages

3-16

References

ISO/IEC. <i>Guide to the Expression of Uncertainty in Measurement.</i> (1995). Geneva. ; Zhang N. (2006), Calculation of the uncertainty of the mean of autocorrelated measurements, Metrologia, 43, doi.org/10.1088/0026-1394/43/4/S15 ; Dorozhovets M. (2007), Upgrading calculating methods of the uncertainty of measurement results in practice, Przegląd Elektrotechniczny, 83, 1. ; Witt T. (2007), Using the autocorrelation function to characterize time series of voltage measurements, Metrologia, 44, 201. ; Kirkup L. (2006), An Introduction to the Uncertainty in Measurement. ; Freund R. (2006), Regression Analysis. Statistical Modeling of a Response Variable. ; Priestley M. (1981), Spectral Analysis and Time Series. ; Box G. (1944), Time Series Analysis: Forecasting and Control. ; Brockwell P. (1991), Time series: theory and methods. ; Anderson T. (1971), The Statistical Analysis of Time Series. ; Bendat J. (1971), Random data: Analysis and measurement procedures. ; Yaglom A. (1987), Correlation theory of stationary and related random processes. ; Bartels J. (1935), Zur Morphologie geophysikalischer Zeitfunktionen, Sitz.-Ber. Preuss. Akad. Wiss, 30, 504. ; Bayley G. (1946), The Effective Number of Independent Observations in an Autocorrelat-ed Time-Series, J. Roy. Stat. Soc. Suppl, 8, 184. ; Bagrov N. (1969), On the equivalent number of independent data, Tr. Gidrometeor. Cent, 44, 3. ; Lubman D. (1969), Spatial Averaging in a Diffuse Sound Field, J. Acoust. Soc. Am, 46, 532. ; Leith C. (1973), The standard error of time-averaged estimates of climatic means, J. Appl. Meteorol, 12, 1066. ; Taubenheim J. (1974), On the significance of the autocorrelation of statistical tests for averages, meansquare deviations and superposed epochs [geophysical data], Gerlands Beitr. Geophysik, 83, 121. ; Şen Z. (1998), Small sample estimation of the variance of time-averages in climatic time series, Int. J. Climatol, 18, 1725. ; Fortus M. (1999), Equivalent Number of Independent Observations: A Review, Izvestia AN. Fizika Atmosf. Okeana, 35, 725. ; That useful approximate form of Eq. (12) was introduced by Bealey and Hammersley [14]. However, because of an error by a factor of two, approximate formulae for <i>n_eff</i> and <i>V_eff</i> given at p. 185 of their paper are incorrect. ; Zięba A. (2008), Uncertainty of the mean of correlated observations, null, 15. ; Law A. (2000), Simulation Modelling and Analysis, 251. ; <a target="_blank" href='http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation'>http://en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation</a> ; Incorrect version of Eq. (31) is given in [14]. See remark [21]. ; Barlett M. (null), On the theoretical specification and sampling properties of autocorrelated time-series, J. Roy. Stat. Soc. Suppl, 8, 27. ; Zięba, A., Ramza, P. In preparation. ; Cox M. (2006), The generalized weighted mean of correlated quantities, Metrologia, 43. ; Cliff A. (1975), The comparison of means when samples consist of spatially autocorrelated observations, Environment and Planning A, 7, 725. ; Bretherton C. (1999), The Effective Number of Spatial Degrees of Freedom of a Time-Varying Field, J. Climate, 12, 1990. ; Zhang N. (2008), Allan variance of time series models for measurement data, Metrologia, 45, 549.

Open Access Policy

Metrology and Measurement Systems is an open access journal with all content available with no charge in full text version.


The journal content is available under the license CC BY-NC-ND 4.0. https://creativecommons.org/licenses/by-nc-nd/4.0/