Table 4: DFA of the series with correlated trend $A{\left[X\left(i\right)\right]}^{p},$ that is, $Y\left(i\right)\mathrm{ }=X\left(i\right)+\mathrm{ }A{\left[X\left(i\right)\right]}^{p}$$p<1$. We pick four values of $p$ as below.
 DFA1 DFA2 DFA3 DFA4 DFA5 $p=\mathrm{ }-3$ ${\alpha }_{0}^{\left(n\right)}$ 0.6713 0.6261 0.6121 0.6317 0.6414 ${s}_{1x}^{\left(n\right)}$ 84 98 146 234 274 ${\alpha }_{1}^{\left(n\right)}$ 1.1376 1.2730 1.3603 1.4800 1.4869 ${s}_{2x}^{\left(n\right)}$ 406 556 704 892 965 ${\alpha }_{2}^{\left(n\right)}$ 0.1524 0.1429 0.1242 0.1267 0.1299 $P=\mathrm{ }-1$ ${\alpha }_{0}^{\left(n\right)}$ 0.6710 0.6260 0.6120 0.6315 0.6412 ${s}_{1x}^{\left(n\right)}$ 84 98 146 234 274 ${\alpha }_{1}^{\left(n\right)}$ 1.1364 1.2713 1.3584 1.4778 1.4847 ${s}_{2x}^{\left(n\right)}$ 406 556 704 892 965 ${\alpha }_{2}^{\left(n\right)}$ 0.1530 0.1434 0.1245 0.1270 0.1301 $P=-0.5$ ${\alpha }_{0}^{\left(n\right)}$ 0.6711 0.6260 0.6120 0.6315 0.6412 ${s}_{1x}^{\left(n\right)}$ 84 98 146 234 274 ${\alpha }_{1}^{\left(n\right)}$ 1.1371 1.2722 1.3594 1.4791 1.4860 ${s}_{2x}^{\left(n\right)}$ 406 556 704 892 965 ${\alpha }_{2}^{\left(n\right)}$ 0.1527 0.1432 0.1244 0.1269 0.1300 $p=0.5$ ${\alpha }_{0}^{\left(n\right)}$ 0.6746 0.6276 0.6131 0.6330 0.6429 ${s}_{1x}^{\left(n\right)}$ 84 98 146 234 274 ${\alpha }_{1}^{\left(n\right)}$ 1.1522 1.2937 1.3835 1.5068 1.5143 ${s}_{2x}^{\left(n\right)}$ 406 556 704 892 965 ${\alpha }_{2}^{\left(n\right)}$ 0.1460 0.1379 0.1210 0.1244 0.1284