Table 4: DFA of the series with correlated trend $A{[X(i)]}^p,$ that is, $Y(i)\mathrm{\hspace{0.17em}\hspace{0.17em}}=X(i)+\mathrm{\hspace{0.17em}\hspace{0.17em}}A{[X(i)]}^p$$p<1$. We pick four values of $p$ as below.

DFA1 DFA2 DFA3 DFA4 DFA5 $p=\mathrm{\hspace{0.17em}\hspace{0.17em}}-3$ ${\alpha }_0^{(n)}$ 0.6713 0.6261 0.6121 0.6317 0.6414 $s_{1x}^{(n)}$ 84 98 146 234 274 ${\alpha }_1^{(n)}$ 1.1376 1.2730 1.3603 1.4800 1.4869 $s_{2x}^{(n)}$ 406 556 704 892 965 ${\alpha }_2^{(n)}$ 0.1524 0.1429 0.1242 0.1267 0.1299 $P=\mathrm{\hspace{0.17em}\hspace{0.17em}}-1$ ${\alpha }_0^{(n)}$ 0.6710 0.6260 0.6120 0.6315 0.6412 $s_{1x}^{(n)}$ 84 98 146 234 274 ${\alpha }_1^{(n)}$ 1.1364 1.2713 1.3584 1.4778 1.4847 $s_{2x}^{(n)}$ 406 556 704 892 965 ${\alpha }_2^{(n)}$ 0.1530 0.1434 0.1245 0.1270 0.1301 $P=-0.5$ ${\alpha }_0^{(n)}$ 0.6711 0.6260 0.6120 0.6315 0.6412 $s_{1x}^{(n)}$ 84 98 146 234 274 ${\alpha }_1^{(n)}$ 1.1371 1.2722 1.3594 1.4791 1.4860 $s_{2x}^{(n)}$ 406 556 704 892 965 ${\alpha }_2^{(n)}$ 0.1527 0.1432 0.1244 0.1269 0.1300 $p=0.5$ ${\alpha }_0^{(n)}$ 0.6746 0.6276 0.6131 0.6330 0.6429 $s_{1x}^{(n)}$ 84 98 146 234 274 ${\alpha }_1^{(n)}$ 1.1522 1.2937 1.3835 1.5068 1.5143 $s_{2x}^{(n)}$ 406 556 704 892 965 ${\alpha }_2^{(n)}$ 0.1460 0.1379 0.1210 0.1244 0.1284