Effect of Trends on Detrended Fluctuation Analysis of Precipitation Series

Table 2

Scaling exponents ${\alpha }^{(n)}$ and crossover times $s_x^{(n)}$ of the series with correlated trends $A{[X(i)]}^p\text{,}$$A=1$ and $p$ are integers from 1 to 6.

		DFA1	DFA2	DFA3	DFA4	DFA5
$p=1$	${\alpha }_0^{(n)}$	0.6718	0.6263	0.6122	0.6318	0.6415
	$s_{1x}^{(n)}$	84	98	146	234	274
	${\alpha }_1^{(n)}$	1.1407	1.2772	1.3650	1.4857	1.4927
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.1512	0.1419	0.1236	0.1263	0.1296
$P=2$	${\alpha }_0^{(n)}$	0.6153	0.5927	0.5856	0.5966	0.6073
	$s_{1x}^{(n)}$	106	116	146	234	274
	${\alpha }_1^{(n)}$	0.8732	0.9452	0.9890	1.0643	1.0593
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.2680	0.2256	0.1687	0.1583	0.1544
$P=3$	${\alpha }_1^{(n)}$	0.6031	0.6021	0.6015	0.6026	0.6024
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.3361	0.2772	0.2224	0.2151	0.2197
$P=4$	${\alpha }_1^{(n)}$	0.5499	0.5570	0.5565	0.5600	0.5633
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.3709	0.3198	0.3010	0.3008	0.3073
$P=5$	${\alpha }_1^{(n)}$	0.5271	0.5367	0.5365	0.5407	0.5454
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.3951	0.3538	0.3638	0.3672	0.3721
$P=6$	${\alpha }_1^{(n)}$	0.5177	0.5276	0.5279	0.5322	0.5377
	$s_{2x}^{(n)}$	406	556	704	892	965
	${\alpha }_2^{(n)}$	0.4138	0.3760	0.4012	0.4060	0.4106