Nonparametric Statistic and the Runs Test for Stationarity - Signal Processing of Random Physiological Signals - page 61

2. That any given sample record is very long compared to the lowest frequency

component in the data, excluding a nonstationary mean. What is meant by
this assumption is that the sample record has to be long enough to permit
nonstationary trends to be differentiated from the random fluctuations of the
time history.

3. That any nonstationarity of interest will be revealed by time trends in the mean

square value of the data.

With these assumptions, the stationarity of random data can be tested by investigating
a single long record, x ( t ), by the following procedure:

(1) Divide the sample record into N equal time intervals where the data in each
interval may be considered independent.

(2) Compute a mean square value (or mean value and variance separately) for
each interval and align these samples values in a time sequence as follows:
X 2 X 2 X 2 X 2 , , ,...

N . 1 2 3

(3) Test the sequence of mean square values for the presence of underlying trends
or variations other than those due to expected sampling variations. The fi-
nal test of the sample values for nonstationary trends may be accomplished
in many ways. A nonparametric approach, which does not require knowledge
of the sampling distributions of data parameter, is desirable [3 and 4]. One
such test is the Runs Test. There are other nonparametric tests that may be
used. These tests will be presented in the section on review of nonparametric
statistics.

8.1.2.1 Runs Test
Because of the requirements in testing with parametric statistics, that is, independence
and normality of the distribution, nonparametric statistics are often used. The advantage
of the nonparametric test is that a priori knowledge regarding the distribution is not
necessary.