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Next, we illustrate our approach on the example of the EEG data file that in-
cludes three seizure intervals. The file contains a 16-channel recording of scalp
EEG sampled at the 200 Hz frequency as well as two auxiliary channels, which
were discarded. The instantaneous phase values were estimated from the EEG time
series by means of Hilbert transform, and the resulting phase series were tested
using the ADF test introduced in Section 18.2.1. Specifically, we applied the aug-
mented Dickey-Fuller procedure to test the presence of a unit root in the individual
univariate components of the multiple time series of estimated phases.
The results of our experiments for three consecutive seizures are presented in
Tables 18.1, 18.2, and 18.3, where each table, respectively, summarizes results for
one of the following types of EEG segments:
•
during approximately 2 s immediately preceding a seizure;
•
during a seizure;
•
during approximately 2 s immediately after a seizure.
The channels, for which the ADF unit root test has detected a presence of a unit root
at the significance level
025, are listed as
integrated
. Whereas the channels,
for which the null hypothesis of a unit root has been rejected by the ADF at the
2.5% level, are denoted by
stationary
. Interestingly, when the ADF is applied at a
0.025 significance level, all three seizure segments are considered stable.
α
=
0
.
Table 18.1: Pre-ictal: Results of the ADF unit root tests for each channel during
the segments 2 s immediately
before a seizure
for three consecutive seizures. (The
significance level is set at 2.5%)
Seizure #
Stationary
Integrated
Seizure 1
3,4,5,7,9,10,11,15
1,2,6,8,12,13,14,16
Seizure 2
3,4,6,7,9,10,11,13,15,16
1,2,5,8,12,14
Seizure 3
3,7,9,11,12,13,14,15
1,2,4,5,6,8,10,16
Table 18.2: Ictal: Results of the ADF unit root tests for each channel
during a seizure
for three consecutive seizures. (The significance level is set at 2
.5%)
Seizure #
Stationary
Integrated
Seizure 1
1-16
none
Seizure 2
1-16
none
Seizure 3
1-16
none
Next, we fit vector autoregression to the multiple time series of phase estimates,
for each of three different segments (before, during, and after a seizure) in order
to determine appropriate lag length parameter
p
. To find appropriate lags
p
,the
