Analysis of detrended time-lagged cross-correlation between two nonstationary time series

• Detrended time-lagged cross-correlation analysis between time series is studied.
• Time-lagged DCCA cross-correlation coefficient is defined and applied in meteorology.
• ρ(n,τ,R,R′)ρ(n,τ,R,R′) is attributed to time delay effect and ρDCCAρDCCA.
• Contribution to ρ(n,τ,R,R′)ρ(n,τ,R,R′) from ρDCCAρDCCA is greater for τnτ>n.

A time-lagged DCCA cross-correlation coefficient is proposed with objective of quantifying the level of time-lagged cross-correlation between two nonstationary time series at time scales. This coefficient, ρ(n,τ,R,R′)ρ(n,τ,R,R′), is defined based on a DCCA cross-correlation coefficient ρDCCA(n)ρDCCA(n). The implementation of this coefficient will be illustrated through selected time series of wind speed and air pollution index (API). The results indicate that both time scales and time lags are very small, ρ(n,τ,R,R′)ρ(n,τ,R,R′) is attributed to a time-lagged effect; while when time lags are comparatively large, ρDCCA(n)ρDCCA(n) contributes partially to ρ(n,τ,R,R′)ρ(n,τ,R,R′). This partial contribution is greater when τnτ>n. ρ(n,τ,R,R′)ρ(n,τ,R,R′) is applied in meteorology. It is found that the method is reasonable and reliable. Therefore, the detrended time-lagged cross-correlation analysis can be useful to deepen and broaden our understanding of cross-correlations between nonstationary time series.