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| - I. Correlated observations
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| - New insights into time series analysis
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| - Context. The first step when investigating time varying data is the detection of any reliable changes in star brightness. This step is crucial to decreasing the processing time by reducing the number of sources processed in later, slower steps. Variability indices and their combinations have been used to identify variability patterns and to select non-stochastic variations, but the separation of true variables is hindered because of wavelength-correlated systematics of instrumental and atmospheric origin or due to possible data reduction anomalies. Aims. The main aim is to review the current inventory of correlation variability indices and measure the efficiency for selecting non-stochastic variations in photometric data. Methods. We test new and standard data-mining methods for correlated data using public time-domain data from the WFCAM Science Archive (WSA). This archive contains multi-wavelength calibration data (WFCAMCAL) for 216,722 point sources, with at least ten unflagged epochs in any of five filters (YZJHK), which were used to test the different indices against. We improve the panchromatic variability indices and introduce a new set of variability indices for preselecting variable star candidates. Using the WFCAMCAL Variable Star Catalogue (WVSC1) we delimit the efficiency of each variability index. Moreover we test new insights about these indices to improve the efficiency of detection of time-series data dominated by correlated variations. Results. We propose five new variability indices that display high efficiency for the detection of variable stars. We determine the best way to select variable stars with these indices and the current tool inventory. In addition, we propose a universal analytical expression to select likely variables using the fraction of fluctuations on these indices ( ffluc). The ffluc can be used as a universal way to analyse photometric data since it displays a only weak dependency with the instrument properties. The variability indices computed in this new approach allow us to reduce misclassification and these will be implemented in an automatic classifier which will be addressed in a forthcoming paper in this series.
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