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Using principal component analysis (PCA), scientists are extracting temporal and spatial patterns in time series of monthly surface air temperature anomalies from 48-high latitude monitoring stations. This requires the adaptation of the standard formulation of PCA to take into account that: (1) there are missing observations in some of the time series; and (2) the time series for the individual stations differ in length considerably.
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To handle (1), we are using a "multiple imputation" approach in which gaps are filled using simulated values that are generated in accordance with a nominal statistical model for each time series (e.g., an autoregressive or fractionally differenced model). We can assess the uncertainty that is due to the gaps by examining the resulting PCAs from many different simulations. To handle (2) we are investigating schemes for combining PCAs based upon overlapping time series of different lengths. We also consider other analysis techniques that have the potential to extract temporal and spatial patterns (e.g., a wavelet scheme in which localized variations in time at a particular temporal scale are compared across the different stations).
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