Cointegration Results

7/30/2019 Cointegration Results

1/9

RESEARCH METHODS IN FINANCE

Assignment-01

Submitted To:

Dr Arshad Hassan

Submitted By:

Sohail Rizwan

Reg # PM123012

Sec # 01


2/9

CO-INTEGRATION

Sense of co-movement by graph:

Using the above graphical analysis we observe a sense of co-movement between the two selected series

i.e. Shangai Stock Exchange and Six Swiss exchange-VTX.

0

1

2

3

4

5

6

7

8

9

10

Ln SSE

Ln VTX


3/9

Unit Root Analysis

A. Shangai Stock Exchange (SSE)Trend and Intercept at level:

Null Hypothesis: SSE has a unit rootExogenous: Constant, Linear Trend

Lag Length: 0 (Automatic - based on SIC, maxlag=15)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -3.479447 0.0436

Test critical values: 1% level -3.992283

5% level -3.426494

10% level -3.136480

*MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(SSE)

Method: Least Squares

Date: 08/31/13 Time: 02:07

Sample (adjusted): 2 272

Included observations: 271 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

SSE(-1) -0.064808 0.018626 -3.479447 0.0006

C 0.435508 0.117134 3.718027 0.0002

@TREND(1) 0.000314 0.000170 1.850427 0.0654

R-squared 0.051382 Mean dependent var 0.010264Adjusted R-squared 0.044303 S.D. dependent var 0.134076

S.E. of regression 0.131072 Akaike info criterion -1.215127

Sum squared resid 4.604226 Schwarz criterion -1.175251

Log likelihood 167.6497 Hannan-Quinn criter. -1.199116

F-statistic 7.258104 Durbin-Watson stat 2.069614

Prob(F-statistic) 0.000852

Interpretation: At first step of Unit Root Analysis, trend and intercept is observed insignificant at level

which suggests using trend further for the detection of data stationarity whether resulting at level or first

difference.


4/9

Intercept at level:

Null Hypothesis: SSE has a unit root

Exogenous: Constant


t-Statistic Prob.*



5% level -2.872001

10% level -2.572417



Dependent Variable: D(SSE)


Date: 08/31/13 Time: 02:08Sample (adjusted): 2 272



SSE(-1) -0.037246 0.011234 -3.315579 0.0010

C 0.279174 0.081498 3.425519 0.0007

R-squared 0.039262 Mean dependent var 0.010264

Adjusted R-squared 0.035690 S.D. dependent var 0.134076






Interpretation: At second step of Unit Root Analysis, intercept is found significant at level which

suggests using trend further for the detection of data stationarity. And, Augmented Dickey-Fuller test

statistic is also significant which proves that data is stationary at level in this series (SSE).


5/9

B. Six Swiss Exchange-VTXTrend and Intercept at level:

Null Hypothesis: VTX has a unit root

Exogenous: Constant, Linear Trend


t-Statistic Prob.*



5% level -3.426557

10% level -3.136516



Dependent Variable: D(VTX)

Method: Least SquaresDate: 08/31/13 Time: 02:10

Sample (adjusted): 3 272



VTX(-1) -0.015686 0.008593 -1.825425 0.0691

D(VTX(-1)) 0.157771 0.059857 2.635798 0.0089

C 0.135683 0.068118 1.991895 0.0474

@TREND(1) 2.16E-05 5.29E-05 0.408646 0.6831








Interpretation: At first step of Unit Root Analysis, trend and intercept is found insignificant at level

which suggests using trend further for the detection of data stationarity whether resulting at level or first

difference.


6/9

Intercept at level:

Null Hypothesis: VTX has a unit root

Exogenous: Constant


t-Statistic Prob.*



5% level -2.872041

10% level -2.572439



Dependent Variable: D(VTX)





VTX(-1) -0.013079 0.005746 -2.276023 0.0236

D(VTX(-1)) 0.155470 0.059499 2.613011 0.0095

C 0.116417 0.049090 2.371529 0.0184








Interpretation: At second step of Unit Root Analysis, intercept is found significant at level which

suggests using trend further for the detection of data stationarity. And, Augmented Dickey-Fuller test

statistic is insignificant which directs using the same assumption of intercept at first difference on the

series.


7/9

Intercept at first difference:

Null Hypothesis: D(VTX) has a unit root

Exogenous: Constant


t-Statistic Prob.*



5% level -2.872041

10% level -2.572439



Dependent Variable: D(VTX,2)





D(VTX(-1)) -0.835427 0.059825 -13.96447 0.0000

C 0.004866 0.002786 1.746595 0.0819

R-squared 0.421174 Mean dependent var -0.000382







Interpretation: Using intercept at first difference in this analysis, Augmented Dickey-Fuller test statistic

found significant which proves that the series (SSE-VTX) is stationary at first difference.

Decision of using ARDL-approach: As both the series i.e. SSE and SSE-VTX are stationary at different

levels, ARDL approach will be used consequently to study the co-movement of the said series.


8/9

ARDL approach Results

Estimates of ARDL regression:

Autoregressive Distributed Lag Estimates

ARDL(1,0) selected based on Schwarz Bayesian Criterion*******************************************************************************

Dependent variable is X1

271 observations used for estimation from 1991M2 to 2013M8*******************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]

X1(-1) .92918 .017501 53.0934[.000]X2 .061173 .014868 4.1146[.000]

*******************************************************************************

R-Squared .96531 R-Bar-Squared .96518

S.E. of Regression .13046 F-stat. F( 1, 269) 7486.0[.000]

Mean of Dependent Variable 7.2301 S.D. of Dependent Variable .69917

Residual Sum of Squares 4.5783 Equation Log-likelihood 168.4142Akaike Info. Criterion 166.4142 Schwarz Bayesian Criterion 162.8121

DW-statistic 2.0675 Durbin's h-statistic -.58019[.562]

*******************************************************************************

Diagnostic Tests*******************************************************************************

* Test Statistics * LM Version * F Version *

******************************************************************************** * * *

* A:Serial Correlation*CHSQ( 12)= 25.5536[.012]*F( 12, 257)= 2.2297[.011]*

* * * ** B:Functional Form *CHSQ( 1)= .10628[.744]*F( 1, 268)= .10515[.746]*

* * * *

* C:Normality *CHSQ( 2)= 3371.6[.000]* Not applicable ** * * *

* D:Heteroscedasticity*CHSQ( 1)= 9.4588[.002]*F( 1, 269)= 9.7285[.002]*

*******************************************************************************A:Lagrange multiplier test of residual serial correlation

B:Ramsey's RESET test using the square of the fitted values

C:Based on a test of skewness and kurtosis of residualsD:Based on the regression of squared residuals on squared fitted values


9/9

Long-run Coefficient:

Estimated Long Run Coefficients using the ARDL ApproachARDL(1,0) selected based on Schwarz Bayesian Criterion

*******************************************************************************

Dependent variable is X1271 observations used for estimation from 1991M2 to 2013M8

*******************************************************************************Regressor Coefficient Standard Error T-Ratio[Prob]X2 .86380 .013682 63.1340[.000]

*******************************************************************************

Error Correction Model:

Error Correction Representation for the Selected ARDL Model

ARDL(1,0) selected based on Schwarz Bayesian Criterion*******************************************************************************

Dependent variable is dX1

271 observations used for estimation from 1991M2 to 2013M8

*******************************************************************************

Regressor Coefficient Standard Error T-Ratio[Prob]dX2 .061173 .014868 4.1146[.000]ecm(-1) -.070819 .017501 -4.0466[.000]

*******************************************************************************

List of additional temporary variables created:dX1 = X1-X1(-1)

dX2 = X2-X2(-1)

ecm = X1 -.86380*X2*******************************************************************************

R-Squared .056719 R-Bar-Squared .053212

S.E. of Regression .13046 F-stat. F( 1, 269) 16.1748[.000]Mean of Dependent Variable .010264 S.D. of Dependent Variable .13408

Residual Sum of Squares 4.5783 Equation Log-likelihood 168.4142

Akaike Info. Criterion 166.4142 Schwarz Bayesian Criterion 162.8121DW-statistic 2.0675

*******************************************************************************R-Squared and R-Bar-Squared measures refer to the dependent variable

dX1 and in cases where the error correction model is highly

restricted, these measures could become negative.

Cointegration Results

Documents

Transcript of Cointegration Results