TY - JOUR
N2 - Prior knowledge of the autocorrelation function (ACF) enables an application of analytical formalism for the unbiased estimators of variance s2a and variance of the mean s2a(xmacr;). Both can be expressed with the use of so-called effective number of observations neff. We show how to adopt this formalism if only an estimate {rk} of the ACF derived from a sample is available. A novel method is introduced based on truncation of the {rk} function at the point of its first transit through zero (FTZ). It can be applied to non-negative ACFs with a correlation range smaller than the sample size. Contrary to the other methods described in literature, the FTZ method assures the finite range 1 < neff ≤ n for any data. The effect of replacement of the standard estimator of the ACF by three alternative estimators is also investigated. Monte Carlo simulations, concerning the bias and dispersion of resulting estimators sa and sa(×), suggest that the presented formalism can be effectively used to determine a measurement uncertainty. The described method is illustrated with the exemplary analysis of autocorrelated variations of the intensity of an X-ray beam diffracted from a powder sample, known as the particle statistics effect.
L1 - http://sd.czasopisma.pan.pl/Content/89816/PDF/Journal10178-VolumeXVIII+Issue4_02paper.pdf
L2 - http://sd.czasopisma.pan.pl/Content/89816
PY - 2011
IS - No 4
EP - 529-542
KW - autocorrelated data
KW - time series
KW - effective number of observations
KW - estimators of variance
KW - measurement uncertainty
A1 - Zięba, Andrzej
A1 - Ramza, Piotr
PB - Polish Academy of Sciences Committee on Metrology and Scientific Instrumentation
SP - 529-542
T1 - Standard Deviation of the Mean of Autocorrelated Observations Estimated with the Use of the Autocorrelation Function Estimated From the Data
DA - 2011
UR - http://sd.czasopisma.pan.pl/dlibra/publication/edition/89816
T2 - Metrology and Measurement Systems
DOI - 10.2478/v10178-011-0052-x
ER -