The History Of Impulse Response Function

Published Date: 02 Nov 2017

Descriptive Statistics

KSE

KLSE

Mean

1.000086

1.000059

Median

1.000136

1.000084

Maximum

1.008857

1.028462

Minimum

0.993389

0.973159

Std. Dev.

0.00159

0.001606

Skewness

-0.3513

0.146881

Kurtosis

5.524881

119.7834

Jarque-Bera

706.0418

1401919

Probability

0

0

Sum

2467.211

2467.146

Sum Sq. Dev.

0.006237

0.006362

Observations

2467

2467

For the analysis of the behavior of the stock returns descriptive statistic is a common tool. Descriptive statistics employed on the returns showed that the Karachi stock exchange (KSE) has an average return during the period is 1.000086 percent with the standard deviation of 0.00159 percent. Malaysian stock market (KLSE) has an average return 1.000059 percent with the standard deviation of 0.001606 percent. The average returns of Karachi stock market higher than the Malaysian stock market but the Malaysian stock market a little bit more risky then Karachi stock exchange. Karachi stock is found low risk high returns market between these markets.

Table 2

Correlation

 

KSE

KLSE

KSERET

1

0.014363

KLSERET

0.014363

1

It is evident that there is no significant correlation between Karachi Stock Exchange and Malaysian stock market from results obtained through correlation as shown in the above table there is a low positive correlation between the KSE and Malaysian stock exchange (KLSE). We can conclude on the basis of these results that there are many opportunities for investor of both market to invest in each other market.

Table 3

VAR statistics

Lag

Log L

LR

FPE

AIC

SC

HQ

0

-10.4539

NA

0.003463

0.010117

0.014836

0.011831

1

14529.2

29043.87

2.58E-08

-11.7979

-11.7837

-11.7927

2

14602.81

146.9258

2.44E-08

-11.8544

-11.83084*

-11.84586*

3

14609.7

13.74196

2.43E-08

-11.8568

-11.8238

-11.8448

4

14614.63

9.817637*

2.43e-08*

-11.85753*

-11.8151

-11.8421

5

14616.48

3.683426

2.43E-08

-11.8558

-11.8039

-11.8369

6

14617.86

2.747533

2.44E-08

-11.8537

-11.7923

-11.8314

* indicates lag order selected by the criterion

LR: sequential modified LR test statistic (each test at 5% level)

FPE: Final prediction error

AIC: Akaike information criterion

SC: Schwarz information criterion

HQ: Hannan-Quinn information criterion

To calculate Johansen and Julius (1991) unrestricted VAR is estimated. Lag selection is a pre-requisite in order to employ co-integration test. Schwarz criterion is found minimum at one lag, so one month lag is appropriate lag length.

Table 4

Unit root test statistics

ADF Level

ADF First Diff.

PP Level

PP First Diff.

KSE

-2.21183

-25.7141

-2.29754

-43.5557

KLSE

-1.4476

-30.6121

-1.46474

-60.8654

Critical Values

1%

-3.43281

-3.43281

-3.43281

-3.43281

5%

-2.86251

-2.86251

-2.86251

-2.86251

10%

-2.56733

-2.56733

-2.56733

-2.56733

It is necessary for the data to be stationary of same order while testing co-integration. Above tests ensure that this data is non-stationary at level but becomes stationary at first difference. Augmented Dicky Fuller and Phillip Perron Tests are executed for testing the data stationary and the Phillip Perron Tests is not strict as compared to ( ADF) but both tests confirmed similar results (Dickey & Fuller, 1981). Data is stationery of same order so we can test co-integration between these markets.

Table 5

Multivariate Co-integration

No. of CE(s)

Eigen value

Statistic

Critical Value

Prob.**

None

0.004427

12.685

15.49471

0.1269

At most 1

0.000709

1.748542

3.841466

0.1861

By using the co-integration we analyzed the long run relationship between these two markets. In above Table we summarized the results for multivariate co-integration analysis and no co-integration was found between these markets in the multivariate analysis. It is possible that these two markets are not co integrated in multivariate analysis.

Table 6

Bi-variate Co-integration

No. of CE(s)

Eigen value

Statistic

Critical Value

Prob.**

None

0.004427

10.93646

14.2646

0.1574

At most 1

0.000709

1.748542

3.841466

0.1861

This table represent that there exist not Be – variate co-integration among these markets Karachi stock exchange and Malaysian stock exchange. These results also represent existence of no co-integration and do not show any other flow of information. To prove the direction we need to use the granger caused representation theorem.

Table 7

Granger causality

Null Hypothesis:

Obs

F-Statistic

Probability

KSE does not Granger Cause KLSE

2465

5.91773

0.00273

KLSE does not Granger Cause KSE

2465

2.51007

0.08147

Granger representation theorem says that if co-integration between two time series than granger causality must exist from at least one way. Table 7 report the result of granger causality. Karachi stock market granger cause Malaysian stock market. Malaysian stock market granger causes Karachi stock market. The unidirectional or bidirectional granger causality between Karachi stock exchange and Malaysian stock exchange. The result of the below table shows that there exist unidirectional causality between KLSE and Karachi stock markets.

Impulse Response Function

Impulse response function (IRF) represent that one standard deviation change in one variable will bring what standard deviation change in other variable. Impulse response results mostly used to explore the random shock on the stock exchange markets. It also analyze response of one market innovation its own and due to change shocks and innovation other markets. Moreover, (IRA) also graphically shows that speed of adjustments. The following figure of display the responses of Karachi equity markets towards the Malaysian equity markets. It is clear that the most of the shocks KSE it’s on innovation not due to the KLSE.

Table 8

Variance decomposition of KSE

Period

S.E

KSE

KLSE

1

0.001771

100

0

2

0.001913

99.85418

0.145818

3

0.002054

99.52075

0.479249

4

0.002321

99.59221

0.407786

5

0.002481

99.54956

0.45044

6

0.002634

99.49896

0.501044

7

0.002799

99.49862

0.501385

8

0.002943

99.48256

0.517442

9

0.00308

99.46715

0.532848

10

0.003215

99.46001

0.53999

In simple words variance decomposition may be defined as the decomposition of variance in the variable which is being studied. It results due to its own dynamic behavior due to changes in the other variable. Table 9 represents the variance decomposition of Karachi stock market with the change its own market behavior and do not changes in Malaysian stock markets. From the table we can say that variations of the Karachi stock exchange its own dynamic behavior and Malaysian stock markets no affect it.

Table 9

Variance decomposition of KLSE

Period

S.E

KLSE

KSE

1

0.001576

0.145948

99.85405

2

0.001609

0.484497

99.5155

3

0.001618

1.575507

98.42449

4

0.001623

2.115221

97.88478

5

0.001628

2.64695

97.35305

6

0.001634

3.345771

96.65423

7

0.001639

3.931802

96.0682

8

0.001644

4.511157

95.48884

9

0.001649

5.116239

94.88376

10

0.001654

5.694629

94.30537

Variance decomposition of KLSE shows that variances in Malaysian stock market return are caused by its own dynamic behavior and innovation and due to changes in Karachi stock exchange. From the table we can say that variation of Malaysian stock exchange is due to its own innovation and Karachi stock market has no affect on it.

CONCLUSION

This paper has examined the long run as well as short term relationship between the Karachi equity markets and Malaysian equity markets. Daily time series data of both equity markets (KSE) and (KLSE) are collected by the yahoo finance. It covers the data period of 09 years starting from Jan 2003 to Dec 2012. The correlation results represents that the Karachi stock markets are not correlated with the Malaysian stock markets. This paper shows that the Karachi stock Markets granger caused the Malaysian stock markets. This paper also show that the on the base of trace statistics there is no co integration between the both stock markets. Vector decomposition analysis represents that the changes occur in the KSE due to its own innovation and dynamic behavior while KLSE no effect to use movement. Finally, therefore the fund manger of developed countries is capable getting the advantage of invest in and diversity there investment because no co integration between both equity markets (KSE) and (KLSE).