Table 2 Cross-correlation exponents considering the well W1 and River RI (Wavelet Filter 0.70).

From: Wavelet gated multiformer for groundwater time series forecasting

Method/time-series

Region I

Region II

\({DFA}_1\)/Well 1 (W1) Wavelet fILter 0.70

\(0.115 \pm 0.005\)

\(0.54 \pm 0.02\)

\({DFA}_1\)/River

\(1.44 \pm 0.02\)

\(1.11 \pm 0.02\)

\({DFA}_0\)/Well 1 (W1) Wavelet filter 0.70

\(0.50 \pm 0.02\)

\(0.976 \pm 0.003\)

\({DFA}_0\)/River

\(0.867 \pm 0.007\)

\(0.56 \pm 0.02\)

\({DCCA}_1\)/W1 (Wavelet filter 0.70) and RI

\(0.915 \pm 0.007\)

\(0.939 \pm 0.008\)

\({DCCA}_0\)/W1 (Wavelet filter 0.70) and RI

\(0.768 \pm 0.008\)

\(0.83 \pm 0.01\)

\({DFA}_1\)/Well 8 (W8) Wavelet filter 0.70

\(0.114 \pm 0.005\)

\(0.74 \pm 0.02\)

\({DFA}_1\)/Well 1 (W1)

\(0.145 \pm 0.008\)

\(0.75 \pm 0.01\)

\({DFA}_0\)/Well 8 (W8) Wavelet filter 0.70

\(0.44 \pm 0.01\)

\(0.993 \pm 0.001\)

\({DFA}_0\)/Well 1 (W1)

\(0.39 \pm 0.01\)

\(0.999 \pm 0.002\)