16
Chapter 2: Misuses
Figure 2.2: Rejection rates of the Mann-Kendall test of the null hypothesis
"no trend" when applied to 1000 time series of length n generated by an
AR(1)-process (2.3) with prescribed a. The adopted nominal risk ofthe test
is 5%.
Top: results for unprocessed serially correlated data.
Bottom: results after prewhitening the data with (2.4). (From Kulkarni and
von Storch, 1995)
Rejection Rates of Mann-Kendall Test
For Serially Correlated Dataj Risk 5%
(AR(1)-process with specified alpha)
unfiltered data
0.8 , - - - - - - - - - - - - - - - - - - - - - - -
0 .4
., ...................................... . "
.10
.20
.30
.40
.60
.60
.70
.80
.90
Rejection Rates after Prewhitening
with Estimated alpha.
filtered data
0.2 r - - - - - - - - - - - - - - - - - -------,
0 . 15
0 . 1
.10
.20
.30
.40
.50
.60
.70
.80
.90
alpha
time urin length
_
n • 100 lZ2I n • 200 I±II n • 300 ISS) n • 500 ~ n • 1000