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We then compute the average of the first and second order sample cross-correlations from these contaminated series over the 1000 replicates.
The average sample cross-correlations computed from the corresponding contaminated series with one and two outliers are plotted in the second and third rows, respectively.
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In this paper, we propose a singular spectrum analysis (SSA) method with novel grouping criteria to remove spikes from highly contaminated velocity time series.
The second and third rows of Fig. 3 depict the averages of the robust cross-correlations computed for the same series contaminated with one and two outliers, respectively.
On the other hand, the first cross-correlations of a heteroscedastic series contaminated with one single outlier as big as 15 or 20 could be confused with those of a white noise.
Based on processing the same series of contaminated data sets, the number of missed outliers, the difference of the height parameters, and the elapsed time by each method are compared.
Similar results would be obtained if the series were contaminated with positive outliers but they are not reported here to save space.
However, when the EGARCH series is contaminated by one single negative outlier, the sample cross-correlation is pushed upwards towards zero, as postulated from the theoretical results in Sect.
A similar analysis can be carried out if the series is contaminated by (k=3) consecutive outliers of the same size but different signs to know whether the limit of the cross-correlations is positive or negative.
The MADOCA real-time ephemerides were applied to a kinematic precise point positioning (PPP) (Zumberge et al. 1997) procedure to find that the analyzed PWV time series was contaminated with occasionally occurring unrealistic sharp variations.
On the other hand, when the series is contaminated with two consecutive outliers of different sign, being the first one negative, only the first cross-correlation will be different from zero and approximately equal to ( -0.5) regardless of whether the series is homoscedastic or heteroscedastic.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com