Cointegration Between PEX and EGYPT From Feb 1998 Through April 2012

PLOT pex

PLOT2 egx

7

EMPIRICAL FINDINGS

For determining the effect produced by changes in EGX index on PEX performance (proxied by Al- Quds index), statistical tests in time-series econometric modeling have to be applied, mainly Augmented Dickey-Fuller Unit Root Test (ADF) and Bi-variate Cointegration Tests (ECM). Table 1 and Table 2 below show the results of applieng unit root tests on PEX and EGX at level respectively.

Hypothesis testing is performed to determine the significance level of the unit root test. Table 1 shows the P-values that indicate this level. From Table 1 and Table 2, it is easy to conclude that both PEX and EGX are non-stationary at all lags, while, the P-values from Table 3 and Table 4 show that the first-differenced PEX and EGX series are consistently stationary at all lags. The study finds that both PSE and EGX are integrated at first difference. Hence, the preliminary requirements in Enger-Granger Cointegration procedure have now been fulfilled.

at level (via ADF) PEX

Table 1: Unit Root Test on

root problem) stationary (unit

- : Data series are non H0

: Data series are stationary (no unit root problem) H1

Type Lags p-value Tau

ZERO MEAN

1 0.4452 -0.63

2 0.4535 -0.61

3 0.3836 -0.77

4 0.3587 -0.82

Econometric Modeling

PEX=f(EGX)

Augmented Dickey‐Fuller Unit Root Test (ADF Test)

Forecasting

Causality Test

Error Correction Model (ECM)

Fail

Vector Auto‐Regressive Model(VAR)

End I (0) I(1)

EG Co‐Integration Test

End End

Pass when ê is stationary Data: 1) Monthly Data

8

5 0.4428 -0.63

SINGLE MEAN

1 0.3139 -1.94

2 0.3245 -1.92

3 0.2137 -2.18

4 0.1940 -2.24

5 0.2975 -1.97

TREND

1 0.4744 -2.22

2 0.4859 -2.20

3 0.2819 -2.6

4 0.2154 -2.76

5 0.4025 -2.35

at level (via ADF) EGX

Table 2: Unit Root Test on

stationary (unit root problem) -

: Data series are non Ho

stationary (no unit root problem) : Data series are

Type Lags p-value Tau

ZERO MEAN

1 0.0443 -2.00

2 0.4273 -0.67

3 0.3613 -0.82

4 0.3798 -0.78

5 0.4218 -0.68

SINGLE MEAN

1 0.0104 -3.46

2 0.5085 -1.55

3 0.4035 -1.75

4 0.4166 -1.73

5 0.4725 -1.62

TREND

1 0.0003 -5.04

2 0.5382 -2.11

3 0.3394 -2.48

4 0.3675 -2.42

5 0.4775 -2.22

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(via ADF) PEX

Differenced -

Table 3: Unit Root Test on First

stationary (unit root problem) -

: Data series are non H0

problem) : Data series are stationary (no unit root

Type Lags p-value Tau

ZERO MEAN

1 <0.0001 -8.20

<0.0001 -5.98

<0.0001 -5.20

<0.0001 -5.58

<0.0001 -5.44

SINGLE MEAN

<0.0001 -8.19

<0.0001 -5.97

<0.0001 -5.19

<0.0001 -5.58

<0.0001 -5.44

TREND

<0.0001 -8.18

<0.0001 -5.97

0.000

2

^-5.18

<0.0001 -5.57

<0.0001 -5.44

(via ADF) EGX

Differenced -

Table 4: Unit Root Test on First

stationary (unit root problem) -

: Data series are non Ho

: Data series are stationary (no unit root problem) H1

Type Lags p-value Tau

ZERO MEAN

1 <0.0001 -26.53

<0.0001 -10.06

<0.0001 -8.07

<0.0001 -7.34

<0.0001 -6.90

SINGLE MEAN

<0.0001 -26.47

<0.0001 -10.04

<0.0001 -8.06

<0.0001 -7.33

10

<0.0001 -6.89

TREND

<0.0001 -26.39

<0.0001 -10.01

<0.0001 -8.03

<0.0001 -7.31

<0.0001 -6.88

Now, that the preliminary requirements have been fulfilled. Now, long-run regression is performed on the PEX and EGX data series (based on the model specification). Table 5 shows the results of the regression analysis supporting the rejection of the null hypothesis and suggesting the existence of a statistically significant positive relationship between PEX and EGX. Table 6 and Table 7 show the descriptive statistics and the correlation matrix of the two market indexes respectively. It is clear there exists a strong correlation between PEX and EGX. In order for OLS estimation to be statistically valid, Engle-Granger (1987) suggests that the long-run residuals derived from the long-run regression (r) must be stationary. Hence, the unit root test (via ADF) on the long-run residuals is applied and results are given in Table 8. The long-run residuals (r) are stationary at all lags. Here, two important results are pointed out: (1) as the long-run residuals are proven stationary, the PEX and EGX are considered co-integrated, and (2) PEX and EGX being co-integrated, the Vector Error Correction Model (VECM) can now be applied for further analysis.

ependent variable) Run Regression (PEX = d

- Table 5: Analysis of Long

EGX term relationship exists between PEX and -

: No Long H0

EGX term relationship exists between PEX and -

: Long H1

Variable Parameter Estimate Standard Error t-Value

Intercept 231.4533 19.66420 11.77*

EGX +0.02459 0.00220 11.16*

* Significant at 5% level

Table 6: Descriptive Statistics

Variable N Mean Std Dev Minimum Maximum

PEX

169 394.4641 225.4218 143.51 1295.08

EGX

169 6629.86 5991.95 345.00 28103.00

) 169 Table 7: Pearson Correlation Table (n =

PEX EGX

PEX 1.00000 0.65356

< 0.0001

100

11

EGX 0.65356

< 0.0001 1.00000

Run Residuals (r) -

Table 8: Stationarity Test for Long

stationary) -

: Residuals have a unit root (non H0

: Residuals have no unit root (stationary) H1

Type Lags p-value Tau

ZERO MEAN

0 <0.0001 -6.22

1 0.0004 -3.62

2 0.0276 -2.19

3 0.0027 -3.02

4 <0.0057 -2.78

5 <0.0058 -2.77

Vector Error Correction Model (VECM)

By employing Vector Error Correction technique, the PEX and EGX variables of the model are estimated. The long term and short term responses involving the two tested variables are examined. It was found through Akaike results (AIC) that the optimum lag-length for the tested model lies at lag 2 (VECM technique prefers lower AIC value). The relevant results are summarized in Table 9 below.

Table 9: Vector Error Correction Model at Lag 2 Dependent Variable : dPEX

Variables Parameter Standard Error t-Value P-Value

Intercept 1.3466 3.7647 0.36 0.7210

LdPEX 0.2407 0.0760 3.17 0.0018

Lr -0.0474 0.0244 -1.94 0.0540

LdEGX 0.000912 0.000739 1.23 0.2193

Note: 1. dpex is first difference in PEX, ldpex is lag 1 of first difference in PEX 2. lr is lag 1 residual and ldEGX is lag 1 of first difference in EGX.

The lr is a lag 1 residual derived from VECM (2). This key component in VECM, supports long-term or equilibrium relationship between the two stock exchanges. A statistically significant equilibrium relation between the two stock market indexes exists as observed by lr’s p value in Table 9. Given lr’s parameter value of 0.1053, this figure implies that there is approximately 10.53% speed of adjustment towards equilibrium made by PEX in the system. This adjustment is considered relatively fast and it could be ascribed to the market integration between the PEX and EGX as expected from

101

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many market analysts. Theoretically, higher speed of adjustment is preferred because a statistically reliable endogenous variable should reflect high speed in its equilibrium adjustment.

Table 10

Granger Causality Test (Short-Run Dynamics)

Source DF F-Value Pr > F

Numerator 2 1.34 0.2646

Denominator 160

A statistically significant positive relationship between the two exchange markets is applied by the positive parameter value of EGX ( +0.0028) given in Table 5. This means that the two exchange markets are positively correlated. The existence of long-term significant relationship between the two exchange markets are significant, the presence of a short-term relation between them. Hence, Granger Causality test is conducted. The results are shown in Table 10 above. According to the F-value reported , the alternative hypothesis is rejected, which suggests nonexistence of a short-term relationship between the two exchange markets. In ensuring that the OLS assumptions are put in check, diagnostic tests are carried out on the tested model.

LM Tests for ARCH Disturbances

To examine constant variance of the error terms, LM ARCH test is applied. The test results are shown at 5% significance level at order 11. This indicates that the H0

below supports rejection of in Table 11

residuals are homoscedastic or operating at constant variance.

Disturbances Table 11: LM Tests for ARCH

: Homoscedastic H0

) t ε Constant variance in (

: Heteroscedastic H1

) t ε Inconstant variance in (

Order LM Pr > LM

1 11.5796 0.0007

2 12.7644 0.0017

3 12.9379 0.0048

4 21.1685 0.0003

5 26.3552 < 0.0001

6 26.4306 0.0002

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7 27.3811 0.0003

8 28.3523 0.0004

9 28.3969 0.0008

10 28.5286 0.0015

11 31.6470 0.0009

12 34.1780 0.0006

Test for Normality

A normality test on error terms distribution should be applied before making any statistical inference.

The test statistics explored by the study for normality depend on the distribution function involving Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling statistics.

Table 12: Normality Test run residuals -

Variable: Short

Test Statistic P-Value

Shapiro-Wilk W 0.933015 <0.0001

Kolmogorov-Smirnov D 0.162904 <0.0100

Cramer-von Mises W-Sq .888047 <0.0050

Anderson-Darling A-Sq 4.261113 <0.0050

The null hypothesis states the short-term residuals are normally distributed.

The results are summarized in table 12, showing that the error terms from ECM (2) are not normally distributed for all the four test statistics (see p-value). These findings do not detract from the whole picture, considering the study’s preliminary nature.

Autocorrelation Test

To ensure that all residuals are independent of one another, autocorrelation test is applied to examine any existence of serial correlation among the short-term residuals. Durbin-Watson test results shown in Table 13 support the absence of autocorrelation among the residuals.

Box Test) -

Table 13: Autocorrelation Test (via Ljung Dependent Variable: dPEX

To Lag Pr > ChiSq

103

14

6 0.0806

12 0.0063

18 0.0022

No serial correlation or autocorrelation exists

run Residuals of the Model) -

Chart 2: CUSUM Test (on Short

CUSUM analysis (or cumulative sum of residual test) is an important tool in econometric modeling. It is employed to tackle diagnostic problems related to parameter instability. From Chart 2 above representing CUSUM analysis, existence of parameter (short-run and long-run parameters) stability is confirmed, the short-run residuals lying within the lower and upper boundaries. As a whole, the predictive model developed from this study can be considered credible since no major diagnostic shortcoming were met in the tested model.

Table 14

Simple Impulse Response by Variable

Variable

Response\Impulse

Lag PEX EGX 1 1.14128 0.00048

2 1.04910 0.00073 3 0.92539 0.00960 4 0.81123 0.00113 5 0.71622 0.00127 6 0.63915 0.00138 7 0.57729 0.00147 8 0.52777 0.00154 9 0.48819 0.00160 10 0.45655 0.00164

-40 -30 -20 -10 0 10 20 30 40

time

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

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