Hydrology and Earth System Sciences
www.hydrol-earth-syst-sci.net
1027-5606
1607-7938
11
2
2007
10.5194/hess-11-851-2007
http://www.hydrol-earth-syst-sci.net/11/851/2007/
http://www.hydrol-earth-syst-sci.net/11/851/2007/hess-11-851-2007.html
http://www.hydrol-earth-syst-sci.net/11/851/2007/hess-11-851-2007.pdf
851
862
2007-02-06
Detecting long-memory: Monte Carlo simulations and application to daily streamflow processes
W. Wang
w.wang@126.com
P. H. A. J. M. Van Gelder
J. K. Vrijling
X. Chen
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, China
Faculty of Civil Engineering & Geosciences, Section of Hydraulic Engineering, Delft University of Technology, 2628 CN Delft, Netherlands
The Lo's modified rescaled adjusted range test (R/S test) (Lo, 1991), GPH
test (Geweke and Porter-Hudak, 1983) and two approximate maximum likelihood
estimation methods, i.e., Whittle's estimator (W-MLE) and another one
implemented in S-Plus (S-MLE) based on the algorithm of Haslett and Raftery
(1989) are evaluated through intensive Monte Carlo simulations for detecting
the existence of long-memory. It is shown that it is difficult to find an
appropriate lag q for Lo's test for different short-memory autoregressive
(AR) and fractionally integrated autoregressive and moving average (ARFIMA)
processes, which makes the use of Lo's test very tricky. In general, the GPH
test outperforms the Lo's test, but for cases where a strong short-range
dependence exists (e.g., AR(1) processes with φ=0.95 or even 0.99), the
GPH test gets useless, even for time series of large data size. On the
other hand, the estimates of <i>d</i> given by S-MLE and W-MLE seem to give a good
indication of whether or not the long-memory is present. The simulation
results show that data size has a significant impact on the power of all the
four methods because the availability of larger samples allows one to
inspect the asymptotical properties better. Generally, the power of Lo's
test and GPH test increases with increasing data size, and the estimates of
<i>d</i> with GPH method, S-MLE method and W-MLE method converge with increasing data
size. If no large enough data set is available, we should be aware of the
possible bias of the estimates.
<br><br>
The four methods are applied to daily average discharge series recorded at
31 gauging stations with different drainage areas in eight river basins in
Europe, Canada and USA to detect the existence of long-memory. The results
show that the presence of long-memory in 29 daily series is confirmed by at
least three methods, whereas the other two series are indicated to be
long-memory processes with two methods. The intensity of long-memory in
daily streamflow processes has only a very weak positive relationship with
the scale of watershed.
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