Vol.2, No.5, 400-406 (2010)
Copyright © 2010 SciRes. Openly accessible at http://www.scirp.org/journal/HEALTH/
Cointegration of event-related potential (ERP) signals in
experiments with different electromagnetic field (EMF)
Argiro E. Maganioti1*, Hountala D. Chrissanthi1, Papageorgiou C. Charalabos2,3,
Rabavilas D. Andreas3, Papadimitriou N. George2, Capsalis N. Christos1
1National Technical University of Athens, Department of Electrical Engineering, Division of Information Transmission Systems and
Material Technology, Athens, Greece; *Corresponding Author: roumag@mail.ntua.gr
2Department of Psychiatry, Eginition Hospital, University of Athens, Athens, Greece
3University Mental Health Research Institute (Umhri), Athens, Greece
Received 11 December 2009; revised 20 February 2010; accepted 23 February 2010.
Due to their non-stationarity, ERP signals are
difficult to study. The concept of cointegration
might overcome this problem and allow for the
study of the co-variability between whole ERP
signals. In this context cointegration factor is
defined as the ability of an ERP signal to co-vary
with other ERP signals. The aim of the present
study was to investigate whether the cointegra-
tion factor is dependent on different EMF condi-
tions and gender, as well as the locations of the
electrodes on the scalp. The findings revealed
that women have a significantly higher cointe-
gration factor than men, while all subjects have
increased cointegration factors in the presence
of EMF. The cointegration factor is location de-
pendent, creating a distinct cluster of high coin-
tegration capacity at the central and lateral
electrodes of the scalp, in contrast to clusters of
low cointegration capacity at the anterior and
posterior electrodes There seem to be distinct
similarities of the present findings with those
from standard methodologies of the ERPs. In
conclusion cointegration is a promising tool
towards the study of functional interactions bet-
ween different brain locations.
Keywords: EMF; ERP; Stationarity; Cointegration;
The electroencephalogram (EEG) is a non-invasive tech-
nique, providing a millisecond by millisecond readout of
the brain’s processing of information, and is relatively
inexpensive to implement. Event-related potentials (ERPs)
are a reflection of the brain’s electrical response to stim-
ulation. Typically, the event-related activity is small and
is, thus difficult to view in the single trial. It is usually
covered by the ongoing ‘spontaneous’ EEG. ERPs tech-
niques overcome this initially poor signal to noise ratio
by averaging across many trials, typically from about 15
to several hundred [1].
Both EEG and ERP signals are time series. Stationary
EEG signals are successfully analyzed in the frequency
domain using Fourier transformations [2]. It has been
found that electromagnetic fields (EMF), similar to those
emitted by mobile phones, have a gender specific effect
on the energy of the EEG [3]. However, Fourier trans-
formations cannot be applied on the non-stationary ERP
signals. There are a number of alternative approaches
that overcome the issue of non-stationarity, such as
windowed Fourier [4,5] and wavelet analysis [6,7].
The majority of the studies analysing ERPs focuses on
certain components of the ERP signal (P50, N100, P200,
N200, P300, N400, P600) [8,9], each of which receives a
particular functional interpretation in the physiology of
the brain. Very few analyses have been made employing
the whole time-series and even less regarding the corre-
lation among the activity of different electrodes. The
common methods used for processing ERPs include
coherence [10], regression [11], correlation [12] and
Granger causality [13]. Most of these methods were first
developed in economic sciences.
In the present paper the whole series of the ERP is
employed as a unit and its non-stationarity is taken into
consideration. The approach, based on a concept intro-
duced by Granger in analysing economic time series, is
cointegration [14]. With regards to brain stimuli, cointe-
gration has been used for linear autoregressive EEG
modeling [15] and for utilizing the stationarity of the
EEG multivariate time series (MTS) [16].
A. E. Maganioti et al. / HEALTH 2 (2010) 400-406
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Openly accessible at
In the present study, cointegration is defined as the
ability of two ERP signals to co-vary in time. The aim is
to investigate whether this ability is dependent on different
EMF conditions and gender, as well as the locations of
the electrodes on the scalp.
2.1. Participants
Two different groups of people, who took part in two
separate experiments, were used in this study. The first
group consisted of nineteen healthy individuals (9 men
and 10 women, mean age = 23.3 ± 2.23 years, mean
education = 16.9 ± 1.82 years) and participated in the
first experiment. The participants of the second experi-
ment were twenty healthy individuals (10 men and 10
women, mean age = 22.75 ± 2.71 years, mean education
= 16.3 ± 1.71 years). In both experiments, the male and
female subgroups were homogeneous with regards to
age and educational level. All participants were right-
handed and had no history of any hearing problem. In-
formed consent was obtained from all subjects.
2.2. Experimental Setup and Measurement
The two experiments were in fact the same as far as the
evaluation method is concerned. The subjects were
evaluated with the digit span Wechsler Auditory test [17].
A warning stimulus of either high (3000 Hz) or low fre-
quency (500 Hz) was presented through earphones to the
subjects, who were asked to memorize the numbers that
followed. The warning stimulus lasted 100 msec. A one
second interval followed the onset of the warning
stimulus and then the numbers to be memorized were
presented by a male voice. At the end of the number
sequence presentation, the same signal tone was repeated.
The signals were recorded for a 1500 msec interval,
divided into 500 msec before the warning stimulus (EEG)
and 1000 msec after that (ERP) [3]. The numbers were
recalled by the subject in the same (low frequency tone)
or in the opposite order (high frequency tone) than that
presented to the participant.
The total task consisted of 52 repetitions for a period
of about 45 min. The subjects performed the tasks twice,
with and without radiation, with an interval of two
weeks between the measurements. The order in which
the subject was exposed at the EMF (exposure at the first
or second visit) was random and the subjects were
unaware of the experimental condition.
The only difference between the two experiments was
the frequency of the EMF signal at which the subjects
were exposed. The first experiment involved an antenna
emitting 900 MHz electromagnetic field, with mean
power at 64 mWatt, while in the second one the antenna
used emitted 1800 MHz electromagnetic field, with
mean power at 128 mWatt. In both experiments the sig-
nal was not modulated.
The experimental setup was the same in both cases
and included a Faraday room, which screened any elec-
tromagnetic interference that could affect the measure-
ments. The subjects sat in an anatomical chair and a cer-
tified dipole antenna was fixed near their right ear. Care
was taken so that the distance between telephone and ear
(about 20 cm) was constant during the whole session.
The antenna was driven by a signal generator, which
could be switched on or off.
The electrophysiological signals were recorded with
Ag/AgCl electrodes. Electrode resistance was kept con-
stantly below 5 k. EEG activity was recorded from 15
scalp electrodes (Fp1, F3, C5, C3, Fp2, F4, C6, C4, O1,
O2, P4, P3, Pz, Cz, Fz) based on the International 10-20
system of Electroencephalography [18], referred to both
earlobes. An electrode placed on the subject’s forehead
served as ground. The bandwidth of the amplifiers was
set at 0.05 Hz to 35 Hz. During the administration of
stimuli, the subjects had their eyes closed in order to
minimize eye movements and blinks. Eye movements
were recorded through electro-oculogram (EOG) and
recordings with EEG higher than 75 μV were rejected
which on the average were 2.1 ± 1.4 trials from the total
of 52. Warning stimuli, as well as the numbers to recall
were presented binaurally via earphones at an intensity
of 65dB sound pressure level. The earphones did not
have metal components in order to avoid EMF concen-
tration.The evoked biopotential signal was submitted to
an analogue-to-digital conversion, at a sampling rate of 1
2.3. Data Transformation
For each question 1500 data points, each corresponding
to time segments of 1 msec duration for each electrode
were saved. In order to maximize the signal to noise
ratio for each subject and each channel all values were
average referenced on the basis of the grand average
across the 52 repetitions of the EEG values. This proce-
dure was done separately for each EMF condition in
both experiments. Artifact–contaminated epochs with a
signal deviation of > 75 μV in the EEG or 100 μV in the
EOG were excluded. The final data for analysis for each
subject and condition consists of 1500 amplitude values
for each electrode, expressed in μVolts corresponding to
the 1500 msec of the time period [3].
A representative chart of the primary recordings of the
amplitude values are shown in Figure 1.
2.4. Stationarity and Integration
A strict stationary process is a stochastic process whose
probability distribution does not vary over time; basic
characteristics such as the mean and the vari-
A. E. Maganioti et al. / HEALTH 2 (2010) 400-406
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Figure 1. Representative graph of the 1500 amplitude values
of the electrode Fz.
var t
remain constant over time. Stationary
time series are easier to analyze and forecast, therefore
non-stationary raw data are often transformed, in order
to become stationary. Non-stationary processes contain a
trend. Trend represents a general systematic linear or
non-linear component that changes over time and does
not repeat, or at least does not repeat within the time
range captured by the data. There are two kinds of trend;
deterministic and stochastic. Time series with determi-
nistic trend have constant variance but non-constant
mean, whereas the ones with stochastic trend exhibit
non-constant variance. Some processes may contain both
stochastic and deterministic trends, which means that
they combine a random walk and a deterministic
, plus an error term.
xr tt
 
A non-stationary process with deterministic trend is
transformed into a stationary one by regressing it on
time t. The most common method for removing stochas-
tic trends from a non-stationary process is differencing.
Differencing of a time series t
in discrete time t is the
transformation of the series t
to a new time series
where the values are the differences between
consecutive values of t
dif t
. The th
d fferences of a time
series are described by the following expression:
()( 1)( 1)
dd d
dif difdif
 ,
where the top index d means the order of the difference.
Many time series need to be differenced more than
once in order to achieve stationarity. From this comes
the definition of integration: a time series is said to be
integrated of order d, in short, I(d), if it becomes station-
ary after differencing d times. A series which is I(d) is
also said to have d unit roots.
2.5. Testing for Stationarity: KPSS Test
The KPSS test [20] is commonly used to test for station-
narity in time-series data. Let {xt}, t = 1, 2, …, N, be the
observed series for which we wish to test stationarity.
Assume that the series can be decomposed into the sum
of a deterministic trend, a random walk, and a stationary
error with the following linear regression model
xr t
where rt is a random walk, i.e., rt = rt-1 + ut and ut is
independent identically distributed (iid) N(0, σu
2), βt is a
deterministic trend and εt is a stationary error.
To test in this model if xt is a stationary process, the
null hypothesis will be σu
2 = 0, which means that the
intercept is a fixed element, against the alternative of a
positive σu
2. Under the null hypothesis, in the case of
stationarity, the residuals et (t = 1, 2, …, N) are from the
regression of x on an intercept and time trend, et = εt. Let
the partial sum process of the et be
2 be the long-run variance of et, which is defined
lim N
The consistent estimator of
2 can be constructed
from the residuals et by the equation below [19]
ˆ() ()
where p is the truncation lag, wj( p) is an optional
weighting function that corresponds to the choice of a
special window, e.g., Bartlett window (Bartlett, 1950)
wj( p) = 1 – j/(p+1).
Then the KPSS test statistic is given by
Under the null hypothesis of stationarity,
PSSV rdr,
where V2(r) is the second level Brownian bridge, given
V2(r) = .
()(23)(1)(66)()Brrr BrrBsds
The upper tail critical values of the asymptotic distr-
ibution of the KPSS statistic are given by Kwiatkowski
et al. [20]. It has been shown that KPSS test is the most
powerful test for the stationarity of time series [20,21],
therefore it will used in the present paper.
Further details of the test are given in Zivot and Wang
2.6. Cointegration
Granger and Newbold [22] have proven that using two
I(1) time series, an apparently significant regression and
correlation can be obtained, even if the two time series
are independent. These regression results were coined as
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“spurious regressions”.
In order to overcome this limitation, Granger intro-
duced a new method, based on the notion that a linear
combination between a pair of non-stationary integrated
series can be stationary. This property is known as coin-
tegration [14]. Cointegration is a formulation of the
phenomenon that non-stationary integrated series can
have linear combinations that have a lower degree of
integration than the original series.
In this paper, the tool used for testing the co-variability
of different electrodes is cointegration. The method of
cointegration involves testing whether the residuals from
a cointegrating regression are stationary. Consider two
time series y1t and y2t which are both I(d). In general,
any linear combination of y1t and y2t will be also I(d).
However, if there exists a vector (1, –β)', such that the
linear combination
zya y
is I(d – b), d b 0,then, following Engle and Granger
(1987), y1t and y2t are defined as cointegrated of order (d,
b) denoted yt = (y1t, y2t)' ~ CI(d, b), with (1, –β)' called
the cointegrating vector [23].
2.7. Data Processing
In this study, the ERP signals are being analyzed in
terms of cointegration. More precisely, the stationarity of
the ERPs of each electrode, for all the subjects, is being
examined using the KPSS test. If the ERPs are found to
be non-stationary (which is the case), they are properly
differenced. This procedure is repeated until KPSS test
indicates stationarity. In order to achieve stationarity the
signals were differenced twice or three times. The null
hypothesis of stationarity with upper tail critical value of
the asymptotic distribution of the KPSS statistic 0.119 is
Cointegration is tested for those electrodes that are
integrated of the same order. The two ERPs are being
regressed one against the other and the order of integra-
tion or stationarity of the residuals is tested. If the order
of integration of the residuals is less than that of the two
ERP signals then cointegration exists between the two
variables. A 15 × 15 array is created for each subject in
each condition and if cointegration exists between elec-
trode i and electrode j—provided that the two electrodes
are integrated of the same order—a 1 is placed at the [i, j]
cell. Else, if no such relationship exists, a 0 is placed in
the cell. For each electrode, the respective column is
summed, and the result is a 1 × 15 vector, containing the
exact number of cointegrations for each electrode for the
specific subject. This number is subsequently normal-
ized by dividing by the maximum number of possible
cointegrations (in this case 14). This number is called
Cointegration Factor (CF) of the electrodes. According
to the above, the values of the electrode CF can range
from 0 to 1. In the same way, the mean value of elec-
trode CFs is the Aggregate Cointegration Factor (ACF).
The aggregate CF was subjected to two-way ANOVA
with gender (male, female) and EMF condition (none,
900 MHz, 1800 MHz) as the independent factors. Like-
wise the CFs at the fifteen electrodes were subjected to
MANOVA with the same independent factors. Finally, in
order to examine whether the CF differs among different
electrodes (locations), an ANOVA procedure with repeated
measures was performed for all the subjects and meas-
urements. The statistical significance was set at 0.05.
Univariate analysis of variance with ACF as the dependent
variable and EMF condition (off, 900 MHz, 1800 MHz),
gender (male, female) and their interaction as the inde-
pendent factors revealed a significant EMF effect (F2,77 =
4, p = 0.022) as well as a significant gender effect (F1,77
= 4, p = 0.048), but no interaction effect. Figure 2 helps
to clarify the direction of the differences between EMF
conditions and genders. As post-hoc comparisons with
Bonferroni corrections show, women have in general a
significantly higher ACF than men (p = 0.048). The
presence of radiation increases ACF. As a result ACF in
the presence of 1800 MHz is significantly higher than in
the absence of radiation (p = 0.029).
In order to further qualify the effect of EMF and gender
on CF for each electrode individually, the CFs of the 15
electrodes were subjected to MANOVA with EMF con-
dition (off, 900 MHz, 1800 MHz), gender (male, female)
and their interaction as independent factors. Table 1
shows the significance of their effects on the CF for all
the electrodes. Significant effects are shown in bold.
Once again the variability of the CF of the leads is
mostly due to the effect of EMF conditions and to a
lesser degree of gender differences, while the EMF x
Gender interaction does not have any significant effect.
These effects were more obvious at F3, C5, C3, C6, C4,
O1, P4, Pz and Cz.
Aggregate Cointegration
Off900MHz 1800MHz
EMF Condition
Male Female
Figure 2. Average of the Aggregate Cointegration Factor for
each gender and EMF condition.
A. E. Maganioti et al. / HEALTH 2 (2010) 400-406
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Table 1. Significance of the effects of EMF condition and
gender on the cointegration factor of the electrodes.
EMF Gender EMF x Gender
Lead p-value p-value p-value
Fp1 0.445 0.302 0.300
F3 0.036 0.044 0.430
C5 0.000 0.035 0.218
C3 0.023 0.011 0.517
Fp2 0.561 0.174 0.709
F4 0.174 0.114 0.346
C6 0.045 0.200 0.624
C4 0.005 0.008 0.676
O1 0.023 0.546 0.629
O2 0.457 0.142 0.516
P4 0.035 0.505 0.936
P3 0.067 0.130 0.435
Pz 0.017 0.295 0.775
Cz 0.036 0.027 0.503
Fz 0.249 0.102 0.684
The repeated ANOVA procedure with the CFs at the
fifteen electrodes as the within subjects factor proved
that there exist significant differences between the means
of the CFs at different locations (F14,77 = 3.7, p < 0.001).
As Figure 3 shows high CFs seem to cluster in the
central and lateral electrodes, while electrodes with low
CFs are grouped mainly in the posterior but also the an-
terior electrodes.
As Granger notes, “cointegration signifies co-movements
among trending variables which can be exploited to test
for the existence of equilibrium relationships within a
fully dynamic specification framework” [23]. In the
present study, the cointegration factor was defined as the
ability of ERP signals to co-vary in time. Results showed
that the values of the CFs seem to follow specific pat-
terns forming distinct clusters, which discriminate the
central and lateral electrodes, having relatively high CFs,
from the anterior and posterior ones. Furthermore,
women have a significantly higher CF than men, while
all subjects have increased CFs in the presence of EMF.
The above findings seem to be in congruence with
other findings regarding typical characteristics of the
ERP signal. Specifically, with regards to EMF effects,
EEG studies showed an increase of spectral power in the
Figure 3. Mean values of the cointegration factors at different
locations on the scalp. Red area signifies cointegration factors
greater than 7.5%, while the blue areas contain electrodes with
cointegration factors less than 7.5%.
alpha band [2,24,25], while ERP studies have demon-
strated reduced N100 amplitudes, shortened N100 laten-
cies and prolonged P300 latencies [26]. In this context, it
has been shown that EMF modulated the event-related
desynchronization/synchronization (ERD/ERS) responses
in the approximately 4-8 Hz EEG frequencies [27]. In
view of these collected observations the authors con-
cluded that EMF could influence brain activity through
thermal and non-thermal mechanisms [28,29].
However, a number of studies failed to find EMF
effects upon brain physiology [30,31]. This might be
attributed to the fact that these studies focused not on the
whole ERP recording, but on certain components of ERP.
In contrast, the present study analyzed the total ERP
signal, specifically its cointegration capacity, which is
likely to represent a more valid picture of the effect of
EMF exposure on the ERP.
The gender-related differences of CF may be related
to different strategies activated due to sex-related func-
tional brain organization, as indicated from psychophy-
siological and neurobiological studies [32-35]. There
also appears to be consistent evidence that EEG coher-
ence varies systematically with gender [36].
Finally, the auditory nature of the warning stimuli that
elicit the ERPs might be the possible reason that affects
the ERP activity in the temporo-parietal region [37,38]
creating the distinct clusters of CF presently found.
To the best of our knowledge, this is the first attempt
to apply the concept of cointegration in the study of
co-variability of ERP signals. Cointegration seems to be
a promising tool towards the study of functional interact-
A. E. Maganioti et al. / HEALTH 2 (2010) 400-406
Copyright © 2010 SciRes. http://www.scirp.org/journal/HEALTH/
Openly accessible at
tions between different brain locations. Also, the method
can be applied on EEG data, obtained from different
clinical and technical experimental conditions. Finally, it
is our immediate object to demonstrate the feasibility of
the cointegration method on additional cogntive tasks
that involves activities in the frontal and occipital scalp
locations, using data from ongoing experiments.
The authors would like to thank M. Kyprianou, Scientific Investigator,
Athens, Greece, for his support on the statistical analysis of the experi-
mental results.
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