Intra-Sector Financial Integration; An Empirical Investigation of Telecommunications Stock Prices

International Research Journal of Finance and Economics ISSN 1450-2887 Issue 32 (2009) © EuroJournals Publishing, Inc. 2009 http://www.eurojournals.com/finance.htm

Intra-Sector Financial Integration; An Empirical Investigation

of Telecommunications Stock Prices

Petros M. Migiakis Athens University of Economics and Business

E-mail: [email protected]

Apostolos G. Christopoulos National Kapodistrian, University of Athens

E-mail: [email protected]

Abstract

In this study we investigate the long run interactions among major international telecommunications companies equities in order to trace significant indications of synchronizations in their price determination procedure. Using Johansen’s cointegration Analysis we find strong evidence of existence of common factors in the international telecommunications companies stock prices’ deterministic process, eliminating the idiosyncratic stochastic trends, thus leaving only one common stochastic trend out of the cointegration space, driving all of the system’s variables’ stochastic processes. Specifically serving our aim to trace evidence of integration among the major international telecommunications’ companies stock prices, namely the prices of AT&T, NTT, BT, Deutsche Telecom and France Telecom, we use Cointegration Analysis for non-stationary time series in order to analyze the common stochastic trends and the exogeneity characteristics of the corresponding stock prices for the time period 1999:1 to 2005:12. Keywords: Johansen Cointegration Analysis, Financial Integration, Telecommunications’

Sector 1. Introduction In recent decades financial markets are closely interacting to each other leading to an increase in the interest of researchers towards financial integration. Parallel to this process, the technological evolutions that have contributed to the enhancement of capital flows and financial and economic integration have resulted in an increase of investors’ interest towards the equities of telecommunications companies globally and subsequently towards their stock pricing determination process. The present analysis intends to contribute to the literature of financial integration and to illuminate the long term trend determination process and interactions of the major telecommunication companies. Our motivation stems from the increased interest in academia and financial sector for the examination of financial integration and from the enhanced focus of the investors on the financial characteristics of the telecommunication companies equities and their pricing processes’ characteristics.

Our aim is to examine how closely the major international telecommunications companies’ stock prices interact in order to analyze the common trends among their pricing procedures in the long term and to investigate the adjusting mechanisms to common equilibria in the short term. The subject

International Research Journal of Finance and Economics - Issue 32 (2009) 231

of financial integration has concentrated the interest of numerous researchers that have published their works on the subject. Significant is the work of Bekaert and Harvey (1995), who propose a theoretical framework based on which they have estimated financial integration for various capital markets using stochastic variables that exhibit time varying characteristics, thus tracing indications of major shifts in the capital markets’ behavior towards financial integration. Ilmanen (1995) investigates possible common determinants of returns in various international bond markets, indicating an ongoing process of global integration. Cointegration Analysis seems to be the foundation in order to investigate for financial integration. Studies using Johansen Cointegration Analysis examining financial integration include the work of Kasa (1992), examining various international stock markets through Johansen Cointegration tests for linear combinations of the time series data, Corhay and Urbain (1993) examining the common stochastic trends present in the European stock markets, Arshanappali and Doukas (1993) investigating the major international stock markets’ interactions for the period after the October 1987 crash. More recent research studies towards financial integration through Cointegration Analysis include the work of Centeno and Melo (1999) who investigate integration of the European money and bank loan markets, Masih and Masih (2001) who apply a combination of Cointegration and structural tests in order to examine for interactions among various stock indices both in the short and in the long run. Additionally we refer to Yang et al. (2005) who apply Cointegration Analysis in order to examine the interactions among various international government bond markets by applying recursive Cointegration analysis and Granger causality tests and Silverstovs et al. (2005) whose work combines Principal Components Analysis and Cointegration techniques in a system investigating integration of the international natural gas markets.

As financial markets are the most globalized institutions, it is quite intriguing to determine the strength of interactions among major international companies stock prices. This fact accompanied by the technological revolution that captured the interest of investors in the late 90’s, formulate an interesting platform for investigation of the interactions among major international telecommunications’ equities in their pricing processes. In our study, following the paradigm of previous studies in the subject of financial integration, we trace evidence of financial integration in the pricing process of the equities of the major telecommunications’ companies, by applying Johansen Cointegration Analysis in order to investigate the elimination of idiosyncratic stochastic trends by linear combinations of the data, namely the Cointegration Vectors and the long and short run interactions among the stock prices of the telecommunications companies. Additionally we apply Granger causality tests in order to trace any leader-follower characteristics in the system. The technical aspects of the Cointegration Analysis are analyzed in Section 2 together accompanied by the description of the data, Section 3 presents the empirical results and Section 4 concludes. 2. Data and Methodology Our data set is comprised of the stock prices of the five major telecommunications organizations globally, namely AT&T, NTT, British Telecom, France Telecom and Deutsche Telecom. The data set contains monthly frequency data of the ten year zero coupon bond returns covering the period January 1999 - January 2006. Additionally, as it is a common practice when examining financial securities priced in various currencies, we transform our data in dollars in order to eliminate the fluctuations of the data stemming from the currency pricing processes, constructing thus more comparable time series. However the data is not harmonized against any other source of idiosyncratic fluctuations, as it is our aim to capture the idiosyncratic trends of the series and to investigate their elimination through a Cointegration context as described later on.

232 International Research Journal of Finance and Economics - Issue 32 (2009)

Table 1: Descriptive Statistics of the Data

Variables Mean Std. Dev. Min. Max. ATT 35.068 11.600 21.136 57.088 BT 586.185 361.917 253.103 1599.549 NTT 6601.336 3683.351 2949.170 16962.022 France Telecom 46.403 40.903 7.515 170.992 Deutsche Telecom 25.453 19.649 9.639 94.915

Table 2: Dickey Fuller Unit Root tests

Variables Unit Root Tests Levels*

Unit Root Tests 1st dif.*

Unit Root Tests Levels Lags=5**

Unit Root Tests 1st dif.Lags=5**

ATT -1.381 -8.567 -1.319 -4.207 BT -1.342 -8.227 -1.780 -3.562 NTT -0.830 -7.275 -1.674 -3.347 France Telecom -0.776 -6.674 -1.499 -2.881 Deutsche Telecom -0.893 -6.004 -1.375 -4.193

*Critical Values 1%= -3.506, 5%= -2.895, 10%= -2.584 **Critical Values 1%= -3.511, 5%= -2.897, 10%= -2.585

Table 1 contains the descriptive statistics of the time series (in levels) we use in our analyses. Prior to presenting the technical details of the methodology we use in our analysis we present the results of the stationarity tests we have applied in the time series of the data set. This step, even though not necessary as financial time series are characterized by non stationarity, confirms that we deal with non stationary time series with I(1) characteristics, allowing us to explain in detail the usefulness of the Johansen cointegration Analysis, for non stationary time series, we have applied. Table 2, in the Appendix, presents the Dickey Fuller tests results concerning existence of unit roots in the data, both for the levels and for the first differences of the series. We accept a 5% confidence interval and the results indicate existence of a unit root in levels while no unit roots are present in the first differences. Thus, the results of the tests indicate that the time series that comprise our data set are non stationary time series with I(1) characteristics.

The methodology we apply is the cointegration Analysis methodology introduced by the influential work of Granger (1983) and Engle and Granger (1987) and advanced further by Johansen (1991, 1992) and Johansen and Juselius (1992). The cointegration Analysis for non-stationary time series investigates the stochastic characteristics of the differenced time series and examines the existence of linear combinations that would allow the series to be commonly integrated with order one eliminating, thus, some of the stochastic trends that would else drive the series. Specifically we would describe the stochastic behavior of the non stationary time series as shown in relation 1.

ttt eXX += −1 (1) After the differentiation of the time series we obtain the I(1) relations 1−−=Δ ttt XXX for the

variables containing the returns of the bond markets that are used to investigate for Cointegration. These relations can be represented by the following equation

Tt

UXXX tt

k

iititt

,...,2,1

,1

11

=

++ΔΓ+Π=Δ ∑−

=−− μ (2)

In relation (2) iΓ and Π are the matrices of the coefficients corresponding to the variables of the system, with rank pp× , while the decomposition of the Π matrix is given by the relation

'αβ=Π , where βα , are vectors of rank rp × . The matrix Π represents the coefficients of the system that give the significance of the cointegration Vectors in each of the equations and iΓ is the matrix of the coefficients of the lagged variables in each of the equations of the system. Specifically


the former coefficient matrix, results in the relations dominating the endogenous variables while the later, results in the relations captured by the VAR between the imposed variables. The vectors that construct the matrix Π , namely vectors α and β capture the short term adjusting behaviour among the data and the long term trending relations respectively. Our estimates stem from the system after restricting the constant in the cointegration space, not including a trending component and imposing ten lags in the VAR of the model.

If all the stochastic trends are eliminated ( pr = ) the time series become stationary, while if no linear combination can be found ( 0=r ), no cointegration exists, indicating strong idiosyncratic stochastic characteristics of the time series and consequently every separate time series is then driven by a separate stochastic trend. In all intermediate occasions between no linear combination and stationarity, the time series are driven by several linear combinations and stochastic trends ( pr <<0 ). Consequently our analysis will begin with the trace of the number of linear combinations, or else cointegration Vectors, that exist in the system. Trace statistic and the maximum eigenvalue ( max−λ ) tests, both introduced in Johansen and Juselius (1990), will serve as the techniques that we will follow to specify the number of Cointegration Vectors. However as most previous researchers, we will mostly rely on the results of the trace statistic tests. The representations of the tests are as follows:

0,...,2,1

)1log(1

−−=

−−= ∑+=

ppr

TTrace i

p

riλ

(3)

and )1log( 1max +−−= rT λλ (4)

In the above formulas λ stands for the eigenvalues and refers to the eigenvalue given for each additional linear combination of the stochastic time series imposed in the system of variables. In the current application of the Johansen cointegration Analysis we apply the cointegration Rank tests as described for the system given that there is no trend and that the constant is restricted in the cointegration space and the critical values that are equivalently used are those referred as case IV in the work of MacKinnon et al. (1999).

Ultimately, in a system that is fully integrated it would be rational to expect a single stochastic trend dominating the system and driving commonly the stochastic processes of all the financial time series of the markets under examination. In more details if the Telecommunications companies’ stock prices were to be fully integrated, our rank test findings should indicate that a common stochastic trend is present and all the other separate stochastic processes are contained in linear combinations or cointegration Vectors obtaining, therefore, the result 1=− rp where p stands for the number of the equations of the system and r is the number of linear combinations that make the system to be integrated of order one. Following previous researchers’ work (e.g Haug et al. 2000), we will accept full integration should the cointegration space is found to leave a single common stochastic trend to drive the markets contained in this analysis; that is if the Trace tests indicate an acceptance of the

1=− rp hypothesis. Should this assumption not be confirmed, only partial integration will be accepted to hold. This hypothesis is based on the reasoning that if all, but one, the I(1) remaining differences among the variables contained in the Cointegration vectors are stationary then the system is driven by a single stochastic trend towards the long run. Thus while we do not expect for the financial time series data to exhibit stationary characteristics, once imposed in the Cointegrating system, we accept that only if common stochastic process characteristics exist, do we accept that the variables of the system are closely connected in their behaviour the long run.

Additionally we examine the hypothesis of weak and strong Exogeneity (Engle et al. 1983, Johansen 1992) in order to investigate further any idiosyncraticities, should they be presented by a not fully integrated system. The formula of the weak exogeneity test is presented in Johansen (1992) and is given by relation (5).


)(~1

1ln 2^

~

rpXTr

ii

i∑ ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−

−

λ

λ (5)

The test of weak exogeneity (relation 5) examines the null hypothesis 0: =aH where the alpha matrix has been described as the matrix of the adjustment coefficients in the cointegration Vectors’ coefficients equation. Strong exogeneity, or long run exclusion, will be investigated as well. Strong exogeneity additionally to the restrictions imposed by weak exogeneity, examines the hypothesis of causal characteristics in the relations of the variables under examination.

An important restriction that will be examined by the exogeneity tests is that in a system characterized by strongly connected pricing procedures of the equities, significantly interacting to each other, no stock pricing series should be found not to fulfill the endogenous characteristics. Otherwise, should partial integration result out of the rank tests’ analyses, it would be useful to trace the markets that are interacted with the rest of the system less significantly and that will be the result of the exogeneity tests. Additionally the stochastic trends representation, exhibited by relation (6),

t

t

iit etCuCX ++= ∑

=2

11

(6)

will be our proxy to the factors that have important influence in the non deterministic behavior of the system, accompanied by a more detailed principal component analysis, in order to further examine the main factors that influence the stochastic trends of the system. In relation (6)

1C represents the vector of the weights that correspond to the cyclical behavior of the stochastic trends, which is determined

through the estimation of the residuals of the system ^

iε by the relation ^^

iiu εα ⊥= , while

2C represents the vector of weights that correspond to the linear part of the trends. The final step of the cointegration Analysis is to perform various hypothesis tests. The purpose

of the hypothesis testing is twofold. First we intend to complete the analysis by confirming through testing theoretically imposed hypotheses of the characteristics of the system used and secondly we investigate further the dominating relations’ structure in the system. Specifically we investigate the hypothesis of closely interacting relations, indicated by stable relations among the data across time in the stock pricing procedures by testing the hypothesis that the stock prices follow a close (1 1) procedure. The hypothesis will be tested by normalizing the β coefficients of the cointegration vectors against the ATT stock price variable, as it is the most eligible candidate for benchmark characteristics. The following matrix represents the restrictions imposed in the β vectors to perform the tests of equilibrium adjustment.

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

1...00

...0.........1...0

0...01

1...11

(7)

The first column of the matrix represents the position of the variable against which we test, the rest of the variables, for equilibrium adjustment. We restrict the β coefficients of that variable to be equal to one and we then restrict the rest of the variables to closely correlate indicating thus that the pricing procedures are strongly affected and short run disequilibria of the variables are absorbed in the long run. The hypotheses’ estimation tests’ statistical properties are given in Johansen (1991) and the tests formula is given by the following relation:

)(~

)(1

)(1ln 2

0

^

1

~

rpX

H

HTr

i

i

i∑⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

−

−

λ

λ (8)


Again the likelihood ratio test examines the eigenvalues of model under the restriction given by the imposed hypothesis relative to the unrestricted model’s eigenvalues and is asymptotically distributed as )(2 rpX where rsprmp )()( −+− are the degrees of freedom of the tests.

At the end of the cointegration Analysis the overall deterministic capability of the system is measured and the analysis concludes with the specification and residual characteristics’ presentation. Finally, we estimate the causality relationships among the five stock prices of the Telecommunications companies included in this analysis by applying Granger causality tests (Granger 1969). The results of the causality tests will enhance our view on the direction of the interactions among the system’s variables. 3. Empirical Results We begin our analysis by presenting the results of the cointegration rank tests and the equivalent critical values. Table 3 reports the values of the Trace and the max eigenvalue tests in order to estimate the number the linear combinations of the data, namely the cointegrating Vectors that exist in the system. The first column indicates the underlying hypothesis for the cointegration Rank while the second and fourth column present the results of the Trace and max eigenvalue tests respectively, which are in their turn compared to the critical values contained in the third and fifth columns.

The results of both the max eigenvalue and the Trace tests indicate that four cointegration Vectors exist in the system of the Telecommunications companies’ stock prices that we examine, thus leaving only one common stochastic trend outside the cointegration space. This is an important finding indicating that the stochastic processes of all the variables of the system are trending towards the same direction, as the linear combinations of the series of the stock prices we examine eliminate all the separate stochastic trends and leave only one common trend outside the cointegration space. Consequently these findings, being indications that the major Telecommunications companies’ stock prices are moving towards the same trends, establish an initial perspective of very close interactions among the series of the stock prices we examine, although substantial is the deeper investigation of the characteristics of these interactions. The findings of the trace and maximum eigenvalues tests are further supported by a recursive cointegration estimation of the system presented by Figures 6, 7 and 8 in the Appendix. The number of variables together with the lags contained in the system permit to estimate the system recursively for the period of 2005:3 – 2006:1. The results indicate that the four linear combinations of the variables contained in the system, persistently formulate significant cointegration vectors for this period, without significant fluctuations, indicating stable cointegrating relations. Table 3: Cointegration rank tests

No of Coint. Vectors ( r ) Trace Test Trace Test Crit. Values* maxλ Test maxλ Test Crit. Values*

1≤r 217.66 88.79 90.24 38.32 2≤r 127.42 63.87 56.91 32.12 3≤r 70.51 42.92 44.18 25.83 4≤r 26.33 25.86 21.88 19.38 5≤r 4.45 12.52 4.45 12.52

*5% MacKinnon Critical Values

Additionally to the cointegration rank tests we examine the exogeneity characteristics of the variables induced in the system in order to obtain a more detailed perspective of the interactions existing in the system. Strongly exogenous tests investigate the potential of long run exclusion of one or more of the variables, while weak exogeneity tests examine the equilibrium adjusting mechanisms. Table 4 presents the results of the exogeneity tests. The exogeneity tests depend crucially on the number of cointegration vectors contained in the system; in this case, as presented above, we have


found that four cointegration Vectors exist in the cointegration space. As presented in Table 4, the result that strong interactions exist among the prices of the Telecommunications companies stock prices, that were found by the cointegration rank tests, are further supported by the Exogeneity tests, as no variable has been found weakly or strongly exogenous to the system. Weak exogeneity tests give indications of disruptions of the significance of the short term coefficients of the cointegration Vectors while strong exogeneity tests indicate limited significance of the long run coefficients of the cointegration Vectors. In this case our findings indicate that in all of the system’s equations there exist significant relations among the variables both in the short and in the long run. More detailed results are reported in Table 5, presenting the decomposition of the cointegration space and the remaining stochastic trend. Table 4: Likelihood Ratio Tests

Variables Weak Exogeneity Test Long Run Exclusion Test )(2 rpX Crit. Val. (4 Coint. Vectors)ATT 45.68 31.01 9.49 BT 47.80 16.50 9.49 Deutsche Telecom 29.30 52.21 9.49 France Telecom 25.65 55.90 9.49 NTT 36.43 24.88 9.49 Constant - 28.46 9.49

The findings of the cointegration rank and the exogeneity tests partly answer to the inquiry of

the degree of integration among the Telecommunications’ companies equities, however the following decomposition of the cointegration space permits to exploit results on the interactions of the series, both in the long run, through theβ vectors and in the short run, through the adjustment variables α . Table 5 reports the coefficients α and β of the cointegration Vectors, thus decomposing the cointegration Vectors. Each vector has been normalized against a different variable of the system, in order to capture the equilibrium adjusting or error correction mechanisms, contained in the vectors of coefficients α and the long run properties of the system through the vectors β respectively. The values of the coefficients are presented under each column where the subscripts indicate the variable used for normalization, while the values in the parentheses indicate statistical significance for the corresponding equilibrium adjusting coefficients.

The vector capturing the greatest impact in the long run is that normalized against the variable of the British Telecom stock price, as the long run coefficients of the rest of the variables contained in this vector have the greatest values among the long run coefficients of the cointegration Vectors. Similarly important, though, are the vectors normalized against the AT&T prices and the prices of Deutsche Telecom’s equity, while the vector capturing the long run effect stemming from the stock price of France Telecom trends is much less important for the system’s long run trend determination. Subsequently we derive an initial result on the directions of the interactions among the telecommunications’ stock prices we examine. The NTT’s equity seems to be less affected from the system’s trends than all the other variables, even though the cointegration vectors significantly affect its price. Our understanding of the interactions among the variables of the system is enhanced by the short run coefficients capturing the equilibrium adjustment properties of each variable against the trends of the system. Specifically the vector of the coefficients α , indicates that AT&T’s stock prices adjust to their own equilibria and to the relative long run equilibrium with British Telecom’s stock price while the same does not hold for the errors occurring among its prices and those of France Telecom and Deutsche Telecom. Similar relations are found in the behaviours of the British Telecom’s stock prices described by the equilibrium adjustment coefficients, as they adjust not only to disequilibria occurring with the AT&T’s stock price but to those among its prices and the Deutsche Telecom’s stock price. France Telecom’s prices exhibit significant adjusting characteristics towards equilibria with AT&T, British Telecom and NTT while they fail to adjust to previous disequilibria


occurring among their stock prices and those of Deutsche Telecom. On the contrary Deutsche Telecom’s prices adjust towards long run equilibria with all the variables of the system. Finally NTT’s stock prices adjust towards long run equilibrium with all the variables of the system except for the AT&T’s stock prices. Indicatively, although there exist variations in the short run interactions among the stock prices of the companies we examine, British Telecom and AT&T are indicated as the sources of the most significant long run trends, a finding that is not only confirmed by the error correction mechanisms but from the long run coefficients as well. Table 5: The Decomposition of the cointegration Space and the Stochastic Trend

ATTβ BTβ FRATELβ DEUTELβ NTTc ATT 1.000 25.617 1.490 -20.773 -170.743 BT 0.279 1.000 -0.052 0.226 -6.505 Deutsche Telecom -18.605 53.925 -1.638 1.000 -196.314 France Telecom 10.876 -179.751 1.000 10.526 139.572 NTT -0.034 0.135 -0.005 -0.077 1.000 Constant 41.946 -401.230 6.354 564.952 -

ATTα BTα FRATELα DEUTELα NTTw -0.023 0.012 -0.005 0.002 ATT (-5.102) (6.429) (0.533) (-0.361) 0.001

-0.365 0.117 0.114 -0.355 BT (-4.376) (3.383) (0.412) (-6.627) -0.001

0.012 0.007 -0.061 -0.006 Deutsche Telecom (2.606) (3.825) (-4.066) (-1.988) 0.002

-0.026 0.014 -0.147 -0.012 France Telecom (-2.382) (3.187) (-4.125) (-1.795) 0.005

-0.479 2.257 8.482 -1.434 NTT (-0.543) (6.166) (2.902) (-2.532) 0.514

The last column of Table 5 reports the eigenvalues NTTc and the loadings NTTw , respectively, of

the moving average of the system which has been normalized against the variable capturing the stock price movements of NTT. The derived values indicate that the stochastic trend, that is left outside the cointegration space, is affected significantly by the variable of the NTT’s prices while the rest of the variables’ loadings are much lower, indicating thus that the procedure determining the moving average of the system is driven by the Japanese company’s stock price rather than by a combination of the system’s variables. Subsequently our indications formulate a system of close interactions among the four variables, namely AT&T, BT, France Telecom and Deutsche Telecom, while the fifth, NTT, is significantly yet not very tightly affected by the rest of the system’s variables.

Table 6 presents the overall impact of the cointegration vectors together with the corresponding significance in each of the systems equations. As indicated previously by the exogeneity tests all the system’s equations are significantly affected by the cointegration vectors, however not in the same fashion. The coefficients of the equations corresponding the impact of the cointegration Vectors represent the product 'αβ=Π of the adjustment coefficients and the equivalent long run coefficients reported in Table 4. As shown in Table 5, the coefficients of the cointegration vectors are significant in the deterministic procedure of the stock prices in all the system’s variables’ equations. The cointegration equations contain significant coefficients from all the variables of the system in the equation of AT&T, France Telecom and Deutsche Telecom. British Telecom’s Cointegration equation and NTT’s cointegration equation are not significantly affected by France Telecom’s variable. Another aspect of the underlying relations captured by the cointegration equations is the negative sign of the Deutsche Telecom’s coefficients in every equation.


Table 6: The Estimates of 'αβ=Π ATT BT Deutsche

Telecom France

Telecom NTT Intercept

0.249 0.006 -1.749 0.415 0.002 -5.027 Δ (ATT) (3.055) (2.523) (-4.960) (3.491) (6.121) (-2.733) 10.175 -0.071 -14.788 -1.281 0.055 -262.059 Δ (BT) (6.860) (-1.552) (-2.301) (-0.591) (7.841) (-7.819) 99.762 1.357 -412.053 109.866 0.388 -1681.836 Δ (Deutsche Telecom) (6.359) (2.805) (-6.062) (4.792) (5.241) (-4.744) 0.223 0.012 -1.406 0.391 0.001 -5.997 Δ (France Telecom) (2.795) (4.972) (-4.062) (3.348) (3.529) (-3.320) 0.378 0.012 -1.855 0.211 0.005 -14.750 Δ (NTT) (1.971) (2.021) (-2.233) (0.754) (5.003) (-3.405)

Table 7 reports the overall deterministic capability of the cointegration equations’ system and

the equivalent short run matrices of the VAR. We have included ten lags in the system in order to eliminate autoregressive characteristics. The upper part of the Table presents the statistics of each of the cointegration equations while the lower part presents the diagnostic tests for autocorrelation and normality. To begin with the later, our system as indicated is not suffering from autocorrelation characteristics and thus is well specified, while the normality checks reject the hypothesis of normal residuals. The equations of the variables catch very large part of the overall pricing processes of the equities under examination. Indicatively, the deterministic parameters obtained by the cointegration analysis and the additional VAR capture approximately 88-96% of the pricing stochastic process. Although ARCH effects are present in our system, the overall presentation of the system’s statistical significance and its deterministic capability are quite well. Table 7: The Deterministic Capability of the Cointegrating System Variables ARCH(10) Normality 2R ATT 9.907 6.140 0.886 BT 19.579 4.221 0.951 NTT 17.416 15.095 0.943 France Telecom 7.076 3.678 0.965 Deutsche Telecom 7.435 0.316 0.945 Diagnostic Tests LM(1)=37.103 LM(4)=15.640 Normality 2X =50.089 p-value 0.06 0.93 0.00

Finally we conduct hypotheses tests towards the overall trending characteristics of the system

and the causality directions of the interactions we have examined insofar. Tables 8 and 9 report the Likelihood Ratio test results and the Granger causality test results respectively. In order to examine the stability of the tight relations in the movements of the stock prices under examination, we impose restrictions in the system, as described by relation 7 in the previous Section. The results reject the hypothesis that the interactions among the prices of the equities we investigate stably interact in a close fashion. The Granger causality tests permit more thorough investigation of the interactions among the stock prices we examine by tracing the causal linkages among the system. Figure 9 presents an illustration of the results of the Granger tests. Our findings indicate that there exist strong bilateral linkages among France Telecom and Deutsche Telecom, Deutsche Telecom and NTT and NTT and British Telecom. Unilateral linkages stemming from British Telecom cause variation on the stock price of Deutsche Telecom while AT&T causes British Telecom’s stock price movements. Finally France Telecom has a causal effect on NTT’s stock price. The findings of the Granger causality indicate that the greatest impact on the system stems from the stock price of British Telecom, confirming thus the findings of the cointegration vectors coefficients.


Table 8: Estimation of the hypothesis of 1 on 1 co movements

The LR-test )4(2X p-value

:0H 1 on 1 Adjustment relations (normalized against ATT)

28.48 0.00

Table 9: Granger Causality Tests p-values reported in brackets

Variables Ψ :0H Variable Ω does not

Granger cause variable Ψ ATT BT Deutsche

Telecom France

Telecom NTT

3.280 1.369 1.521 1.513 ATT - [0.000] [0.188] [0.126] [0.128]

0.961 2.398 1.414 6.127 BT [0.476] - [0.008] [0.168] [0.000]

3.281 1.621 3.182 2.937 Deutsche Telecom [0.000] [0.095] - [0.000] [0.001] 3.289 2.810 5.541 5.897

France Telecom [0.003] [0.002] [0.000] - [0.000] 0.695 2.810 7.949 1.445

Var

iabl

es Ω

NTT [0.729] [0.002] [0.000] [0.155] -

4. Conclusion We have examined the interactions among major international Telecommunications’ companies’ stock prices by applying Johansen cointegration Analysis for non stationary time series. Our results support an enhanced integration pricing framework existing among the system’s variables, as all idiosyncratic stochastic trends have been restricted in the cointegration space leaving only one common stochastic trend outside, indicating that the system is driven by the same stochastic parameters. Consequently we have identified a fully integrated system of interactions among the system’s stock prices while our findings were supported further by the exogeneity tests and the long and short run interactions among the system which were specified by the decomposition of the cointegration vectors’ coefficients indicating strong long run interactions and significant error correction mechanisms towards common equilibria. Finally even though the hypothesis that the strength of interactions is stable among the system’s stock prices, our Granger causality results describe in detail the direction of the linkages among the system’s variables. British Telecom’s stock price evidently Granger causes many of the variations of the system, while a complex net of interactions exist indicating among others that a strong ‘European’ unilateral relation exists among the Deutsche Telecom’s and France Telecom’s stock prices.


References [1] Arshanapalli B. and Doukas J. (1993) ‘International Stock Markets Linkages: Evidence From

the Pre- and Post- October 1987 Period’ Journal of Banking and finance 17 pp.193-208 [2] Baele D., Ferrando A., Hordahl P., Krylova E. and Monnet C. (2004) ‘Measuring Financial

Integration In the Euro Area’ European Central Bank Occasional Paper Series no 14 [3] Bekaert G. and Harvey C. (1995) ‘Time-Varying World Market Integration’, Journal of

Finance Vol. 50 pp.403-444 [4] Centeno M. and Mello A. (1999) ‘How Integrated Are The Money Market And The Bank Loan

Market Within The European Union?’ Journal of International Money and Finance pp.75-106 [5] Corhay A., Tourani Rad A. and Urbain J.-P. (1993) ‘Common Stochastic Trends in European

Stock Markets’ Economics Letters pp. 385-390 [6] Davidson J. and Hall S. (1991) ‘Cointegration In Recursive Systems’ The Economic Journal

pp. 239-251 [7] Dunne P., Moore M. and Portes R. (2002) ‘Defining Benchmark Status: An Application Using

Euro-Area Bonds’ National Bureau of Economic Research, working paper no 9087 [8] Engle R., Hendry D. and Richard J. F. (1983) ‘Exogeneity’ Econometrica pp.277-304 [9] Engle R. and Granger C. W. (1987) ‘Co-Integration and Error Correction: Representation,

Estimation And Testing’ Econometrica pp. 251-276 [10] Granger C. W. (1969) ‘Investigating Causal Relations by Econometric Modeling and Cross-

Spectral Methods’ Econometrica pp.424-438 [11] Ilmanen A. (1995) ‘Time-Varying Expected Returns in International Bond Markets’ Journal of

Finance pp. 481-506 [12] Haug A., MacKinnon J. and Michelis L. (2000) ‘European Monetary Union: A Cointegration

Analysis’ Journal of International Money and Finance v. 19 pp.419-432 [13] Johansen S. and Juselius K. (1992) ‘Testing Structural Hypotheses In A Multivariate

Cointegration Analysis of The PPP And The UIP For UK’ Journal of Econometrics pp. 211-244

[14] Johansen S. and Juselius K. (1994) ‘Identification of The Long-Run And The Short-Run Structure. An Application To The ISLM Model’ Journal of Econometrics pp. 7-36

[15] Johansen S. (1992) ‘Testing Weak Exogeneity And The Order of Cointegration In UK Money Demand Data’ Journal of Policy Modeling pp. 313-334

[16] Johansen S. (1991) ‘Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models’ Econometrica pp. 1551-1580

[17] Juselius K. and MacDonald R. (2004) ‘International Parity Relations Between The USA and Japan’ Japan and The World Economy pp. 17-34

[18] Kasa K. (1992) ‘Common Stochastic Trends in International Stock Markets’ Journal of Monetary Economics 29 pp. 95-124

[19] Katsimbris G. and Miller S. (1993) ‘Interest Rate Linkages Within The European Monetary System: Further Analysis’ Journal of Money, Credit and Banking pp.771-779

[20] MacKinnon J., Haug A. and Michelis L. (1999) ‘Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration’ Journal of Applied Econometrics pp.563-577

[21] Masih R. and Masih A. (2001) ‘Long and Short Term Dynamic Causal Transmission Amongst International Stock Markets’ Journal of International Money and Finance 20 pp. 563-587

[22] Philips P.C. and Ouliaris S. (1990) ‘Asymptotic Properties for Residual Based Tests for Cointegration’ Econometrica pp. 165-193

[23] Silverstovs B., L’Hegaret Guillaume, Neumann A. and von Hirschhausen C. (2005) ‘International Market Integration for Natural Gas? A Cointegration Analysis of Prices in Europe, North America and Japan’ Energy Economics 27 pp.603-615

[24] Vahid F. and Engle R. (1993) ‘Common Trends and Common Cycles’ Journal of Applied Econometrics pp. 341-360


[25] Yang J. (2005) ‘International Bond Markets Linkages: a Structural VAR Analysis’ International Financial Markets, Institutions and Money 15 pp. 39-54

Appendix

Figures 1-5: The Time Series

ATTLEVEL

2000 2001 2002 2003 2004 2005202530354045505560

DIFFERENCE

2000 2001 2002 2003 2004 2005-10.0

-7.5

-5.0

-2.5

0.0

2.5

5.0

7.5

NTTLEVEL

2000 2001 2002 2003 2004 20052500

5000

7500

10000

12500

15000

17500

DIFFERENCE

2000 2001 2002 2003 2004 2005-2000

-1000

0

1000

2000

3000

4000

DEUTEL

LEVEL

2000 2001 2002 2003 2004 20050

25

50

75

100

DIFFERENCE

2000 2001 2002 2003 2004 2005-20-15-10-505

101520


BTLEVEL

2000 2001 2002 2003 2004 2005200400600800

1000120014001600

DIFFERENCE

2000 2001 2002 2003 2004 2005-300

-200

-100

0

100

200

300

FRATEL

LEVEL

2000 2001 2002 2003 2004 20050

255075

100125150175

DIFFERENCE

2000 2001 2002 2003 2004 2005-20

-10

0

10

20

30

40

Figures 6-8: Recursive Estimation of the Cointegration Space

The Trace testsZ(t)

3 2 2 1 1 31 30 29 29 28 28 27March April May June July August September October November December January

0.00.51.01.52.02.53.03.54.0

R(t)

1 is the 10% significance level


0.00.51.01.52.02.53.03.5


lambda1

Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan2005

0.00

0.25

0.50

0.75

1.00

lambda2


0.00

0.25

0.50

0.75

1.00

lambda3


0.00

0.25

0.50

0.75

1.00

lambda4


0.00

0.25

0.50

0.75

1.00

Z(t)

- ln(det(S00))


-16.40

-16.32

-16.24

-16.16

-16.08

-16.00

-15.92

-Sum(ln(1-lambda))

Mar Apr May J un J ul Aug Sep Oc t N ov D ec J an2005

2.75

3.00

3.25

3.50

3.75

4.00

-2/T*log-likelihood


-20

-18

-16

-14

-12

-10

-8

-6

R(t)- ln(det(S00))


-16.40

-16.35

-16.30

-16.25

-16.20

-16.15

-Sum(ln(1-lambda))


2.75

3.00

3.25

3.50

-2/T*log-likelihood


-20

-18

-16

-14

-12

-10

-8

-6

Figure 9: Granger Causality Directions

ATT BT

NTT

France Tel. Deutsche Tel.

Intra-Sector Financial Integration; An Empirical Investigation of Telecommunications Stock Prices

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