Cointegration of event-related potential (ERP) signals in experiments with different electromagnetic field (EMF) conditions

doi:10.4236/health.2010.25060

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Vol.2, No.5, 400-406 (2010)

doi:10.4236/health.2010.25060

Health

Cointegration of event-related potential (ERP) signals in

experiments with different electromagnetic field (EMF)

conditions

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.

ABSTRACT

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;

ACF

1. INTRODUCTION

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

401

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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. METHODS

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

Procedure

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 kΩ. 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

KHz.

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

402

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Figure 1. Representative graph of the 1500 amplitude values

of the electrode Fz.

ance





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

trend





, 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

dif

. 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



,

and



2 be the long-run variance of et, which is defined

lim N

NES







The consistent estimator of



2 can be constructed

from the residuals et by the equation below [19]

111

ˆ() ()

tjtj

pewpe



ttj









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

222

ˆ()

PSS NSp







.

Under the null hypothesis of stationarity,

0()

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

(2002).

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

A. E. Maganioti et al. / HEALTH 2 (2010) 400-406

403

Openly accessible at

“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

12tt

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

tested.

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).

3. STATISTICAL ANALYSIS

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.

4. RESULTS

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.

10%

20%

Aggregate Cointegration

Factor

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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Openly accessible at

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.

5. DISCUSSION

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

405

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.

6. ACKNOWLEDGEMENTS

The authors would like to thank M. Kyprianou, Scientific Investigator,

Athens, Greece, for his support on the statistical analysis of the experi-

mental results.

REFERENCES

[1] Fabiani, M., Gratton, G. and Coles, M. (2000) Event-

related potentials: Methods, theory and applications.

Handbook of Psychophysiology, 3rd Edition. Cambridge

University Press, New York.

[2] Laufs, H., Kleinschmidt, A., Beyerle, A., Eger, E., Salek-

Haddadi, A., Preibisch, C. and Krakow, K. (2003) EEG-

correlated fMRI of human alpha activity. NeuroImage,

19(4), 1463-1476.

[3] Papageorgiou, C.C., Nanou, E.D., Tsiafakis, V.G., Cap-

salis, C.N. and Rabavilas, A.D. (2004) Gender related

differences on the EEG during a simulated mobile Phone

signal. Neuroreport, 15(16), 2557-2560.

[4] Agam, Y. and Sekuler, R. (2007) Interactions between

working memory and visual perception: An ERP/EEG

study. NeuroImage, 36(3), 933-942.

[5] Edwards, E., Soltani, M., Deouell, L.Y., Berger, M.S. and

Knight, R.T. (2005) High gamma activity in response to

deviant auditory stimuli recorded directly from human

cortex. Journal of Neurophysiology, 94, 4269-4280.

[6] Yordanova, J., Rosso, O.A. and Kolev, V. (2003) A tran-

sient dominance of theta event-related brain potential

component characterizes stimulus processing in an audi-

tory oddball task. Clinical Neurophysiology, 11 4(3), 529-

540.

[7] Quiroga, R.Q., Sakowitz, O.W., Basar, E. and Schürmann,

M. (2001) Wavelet Transform in the analysis of the fre-

quency composition of evoked potentials. Brain Re-

search Protocols, 8(1), 16-24.

[8] Chlubnová, J., Kremláček, J., Kubová, Z. and Kuba, M.

(2005) Visual evoked potentials and event related poten-

tials in congenitally deaf subjects. Physiological Re-

search, 54, 577-583.

[9] Sanders, L.D., Newport, E.L. and Neville, H.J. (2002)

Segmenting nonsense: An event-related potential index

of perceived onsets in continuous speech. Nature Neuro-

science, 5, 700-703.

[10] Shibata, T., Shimoyama, I., Ito, T., Abla, D., Iwasa, H.,

Koseki, K., Yamanouchi, N., Sato, T. and Nakajima, Y.

(1998) The synchronization between brain areas under

motor inhibition process in humans estimated by event-

related EEG coherence. Neuroscience Research, 31(4),

265-271.

[11] Hauk, O., Davis, M.H., Ford, M., Pulvermüller, F. and

Marslen-Wilson, W.D. (2006) The time course of visual

word recognition as revealed by linear regression analy-

sis of ERP data. NeuroImage, 30(4), 1383-1400.

[12] Nikolaev, A.R., Ivanitsky, G.A., Ivanitsky, A.M., Posner,

M.I. and Abdullaev, Y.G. (2001) Correlation of brain

rhythms between frontal and left temporal (Wernicke’s)

cortical areas during verbal thinking. Neuroscience Let-

ters, 298(2), 107-110.

[13] Oya, H., Poon, P.W.F., Brugge, J.F., Reale, R.A., Kawa-

saki, H., Volkov, I.O. and Howard III, M.A. (2007) Func-

tional connections between auditory cortical fields in

humans revealed by Granger causality analysis of in-

tra-cranial evoked potentials to sounds: Comparison of

two methods. Biosystems, 89, 198-207.

[14] Engle, R. and Granger, C.W. (1987) Co-integration and

error correction representation estimation and testing.

Econometrica, 55(2), 251-276.

[15] Yang, K. and Shahabi, C. (2005) On the stationarity of

multivariate time series for correlation-based data analy-

sis. Proceedings of the Fifth IEEE International Confer-

ence on Data Mining, 805-808.

[16] Brandt, M.E., Ademoglu, A. and Pritchard, W.S. (2000)

Non-linear prediction and complexity of alpha EEG ac-

tivity. International Journal of Bifurcation and Chaos,

10(1), 123-133.

[17] Wechsler, D. (1955) Manual for the Wechsler adult intel-

ligence scale. Psychological Corporation, New York.

[18] Jasper, H.H. (1958) The ten-twenty electrode system of

the international federation. Electroencephalography and

Clinical Neurophysiology, 10, 371-375.

[19] Newey, W.K. and West, K.D. (1987) A simple, positive

semi-definite, heteroskedasticity and autocorrelation con-

sistent covariance matrix. Econometrica, 55(3), 703-708.

[20] Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin,

Y. (1991) Testing the null hypothesis of stationarity

against the alternative of a unit root. How sure are we

that economic time series have a unit root? Journal of

econometrics, 54, 158-178.

[21] Hobijn, B., Franses, P.H. and Ooms, M. (2004) Gener-

alizations of the KPSS-test for stationarity. Statistica

Neerlandica, 58(4), 483-502.

[22] Granger, C.W. and Newbold, P. (1974) Spurious regres-

sion in econometrics. Journal of Econometrics, 2(2), 111-

120.

[23] Dolado, J.J., Gonzalo, J. and Marmol, F. (2009) A Com-

panion to Theoretical Econometrics, In: Baltagi, B.H.,

Ed., Blackwell Reference Online, 634-654

http://www.blackwellreference.com/public/book?id=g97

81405106764_9781405106764

[24] Croft, R.J., Chandler, J.S., Burgess, A.P., Barry, R.J.,

Williams, J.D. and Clarke, A.R. (2002) Acute Mobile

phone operation affects neural function in humans.

Clinical Neurophysiology, 113(10), 1623-1632.

[25] Curcio, G., Ferrara, M., Moroni, F., D'Inzeo, G., Bertini,

M. and De Gennaro, L. (2005) Is the brain influenced by

a phone call? An EEG study of resting wakefulness.

Neuroscience Research, 53(3), 265-270.

[26] Hamblin, D.L., Wood, A.W., Croft, R.J. and Stough, C.

(2004) Examining the effects of electromagnetic fields

emitted by GSM mobile phones on human event-related

potentials and performance during an auditory task.

Clinical Neurophysiology, 115(1), 171-178.

[27] Krause, C.M., Björnberg, C.H., Pesonen, M., Hulten, A.,

A. E. Maganioti et al. / HEALTH 2 (2010) 400-406

406

Liesivuori, T., Koivisto, M., Revonsuo, A., Laine, M. and

Hämäläinen, H. (2006) Mobile phone effects on chil-

dren's event-related oscillatory EEG during an auditory

memory task. International Journal of Radiation Biology,

82(6), 443-450.

[28] Challis, L.J. (2005) Mechanisms for interaction between

RF fields and biological tissue. Bioelectromagnetics,

Supplement 7 Review, 26, 98-106.

[29] Valentini, E., Curcio, G., Moroni, F., Ferrara, M., De

Gennaro, L. and Bertini, M. (2007) Neurophysiological

effects of mobile phone electromagnetic fields on hu-

mans: A comprehensive review. Bioelectromagnetics, 28,

415-432.

[30] Hamblin, D.L., Croft, R.J., Wood, A.W., Stough, C. and

Spong, J. (2006) The sensitivity of human event-related

potentials and reaction time to mobile phone emitted

electromagnetic fields. Bioelectromagnetics, 27, 265-273.

[31] Yuasa, K., Arai, N., Okabe, S., Tarusawa, Y., Nojima, T.,

Hanajima, R., Terao, Y. and Ugawa, Y., (2006) Effects of

thirty minutes mobile phone use on the human sensory

cortex. Clinical Neurophysiology, 117(4), 900-905.

[32] Skrandies, W., Reik, P. and Kunze, C. (1999) Topography

of evoked brain activity during mentalarithmetic and

language tasks: sex differences. Neuropsychologia, 37(4),

421-430.

[33] Briere, M.E., Forest, G., Chouinard, S. and Godbout, R.

(2003) Evening and morning EEG differences between

young men and women adults. Brain and Cognition,

53(2), 145-148.

[34] Dimpfel, W., Wedekind, W. and Keplinger, I. (2003)

Gender difference in electrical brain activity during

presentation of various film excerpts with different emo-

tional content. European Journal of Medical Research,

8(5), 192-198.

[35] Razumnikova, O.M. and Vol'f, N.V. (2007) Gender dif-

ferences in interhemisphere interactions during distrib-

uted and directed attention. Neuroscience and Behavioral

Physiology, 37(5), 429-434.

[36] Barry, R.J., Clarke, A.R., McCarthy, R., Selikowitz, M.,

Johnstone, S.J. and Rushby, J.A. (2004) Age and effects

in EEG coherence: I. Developmental trends in normal

children. Clinical Neurophysiology, 115(10), 2252-2258.

[37] Haarala, C., Aalto, S., Hautzel, H., Julkunen, L., Rinne,

J.O., Laine, M., Krause, B. and Hämäläinen, H. (2003)

Effects of a 902 MHz mobile phone on cerebral blood

flow in humans: a PET study. Neuroreport, 14(16), 2019-

2023.

[38] Cinel, C., Boldini, A., Russo, R. and Fox, E. (2007) Ef-

fects of mobile phone electromagnetic fields on an audi-

tory order threshold task. Bioelectromagnetics, 28(6), 493-

496.