Nonparametric Statistic and the Runs Test for Stationarity - Signal Processing of Random Physiological Signals - page 66

TABLE 8.2: ( Continued )

α

n = N / 2

0.99 0.975 0.95 0.05 0.025 0.01

50 38 40 42 59 61 63

55 43 45 46 65 66 68

60 47 49 51 70 72 74

65 52 54 56 75 77 79

70 56 58 60 81 83 85

75 61 63 65 86 88 90

80 65 68 70 91 93 96

85 70 72 74 97 99 101

90 74 77 79 102 104 107

95 79 82 84 107 109 112

100 84 86 88 113 115 117

13 falls within the range between 6 and
15; hence, the data are independent and ergodic; thus stationary. There is no reason to
question independence of observations since there is no evidence of an underlying trend.

The hypothesis is accepted, since r =

8.1.2.3 Summary of Ergodic Test Via the Runs Test
The statistical properties of a random process can be determined by computing ensemble
averages at specific instances of time or from segments of a single long record. If the time
averaged mean value , k ) are time invariant

when computed over different sample functions, then the random process is Ergodic and
Stationary. An easier approach in testing a single random signal for stationarity is to use
the Nonparametric Runs Test.

μ x ( k ) and the autocorrelation function R x ( λ