Effect of Outliers and Non-consecutive Data Points on the Detrended Cross-Correlation Analysis

In this paper, we investigate the robustness of the well-known DCCA (detrended cross-correlation analysis) methodology and give a qualitative analysis result. Due to the non-stationarity inherent in most observational data sets, the results of DCCA and its variants may be spurious. In particular, oceanographic data sets contaminated with measurement errors are subject to unusual records, making it difficult to trust DCCA results. To ensure the validity of the DCCA methodology for the oceanographic time series, we conduct simulation studies based on the ARFIMA process and perform statistical tests using surrogate methods. First, so-called outliers due to measurement error lead to the spurious results of DCCA methods while discontinuities in the time series have been found to have little effect on the results. This means that the cross-correlation structure is robust to the discontinuity of time series. Second, statistical significance of cross-correlation was obtained through a surrogate statistical test for the oceanographic time series.