A new methodology for local cross-correlation between two nonstationary time series

To measure the degree of local cross-correlation between two nonstationary time series, a new approach with a locally weighted Pearson correlation coefficient based on a simple locally weighted linear regression model was proposed. In this approach, a Gaussian decay-based function is selected as a weighting function. An appropriate bandwidth is selected using an alternative criterion. Some factors influencing the local cross-correlation degree, including long-range exponent estimated by means of a detrended fluctuation analysis (DFA) and seasonal change in the series, are discussed. Artificial and real-world datasets are analyzed. The results show that the proposed method can measure the degree of a locally intrinsic cross-correlation between two series. The contribution of this locally intrinsic cross-correlation is attributed to original input excitation sources and DFA scaling exponents. The effects of seasonal change with a high-frequency in the series on a locally intrinsic cross-correlation are significant. The effects of a low-frequency seasonal change are insignificant. A positive local cross-correlation between a synchronous wind speed and air pollution index series in Nanjing, China is observed, which is related to externally imported air pollution sources. Consistent results are obtained by comparing the new method with the detrended cross-correlation coefficientρDCCA. Therefore, the proposed approach is reliable, reasonable, and applicable, and can examine the degree of the local intrinsic cross-correlation between two nonstationary time series.