Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series

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