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4.5 Autoregressive models: Such models like autoregressive (AR) model and theexponential generalized autoregressive conditional heteroskedasticity (EGARCH)model are useful to test the impact of Brexit on the dynamic linkages andcausal relationships among the selected stock markets.Table12 depicts  the results of the empiricalanalysis with AR(1)–EGARCH(1,1)  modelsduring        pre-Brexit period.

All thecoef?cients  of the EGARCH term (?) , allcoefficients of asymmetric effects (?) and GED parameter estimates have been found to be  statisticallysigni?cant at the 1% level. Since each of these values  is less than 2, hence we can conclude that tails of the error terms are heavier than tail of the normaldistribution. Evidently it  indicates theexistence of ARCH effects. Moreover, this table indicates the diagnostics statistics of analysis of the AR–EGARCHmodels—the Q(s) and the Q 2(s) .

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The Q statistic at lag s, Q(s), isa test statistic for the null hypothesis that there is no autocorrelation up toorder s for standardized residuals; it is asymptotically distributed aschi-square, with the degrees of freedom equal to the number of autocorrelationless the number of parameters. The Q 2(s)  is that for squared residuals . Result ofthis paper accepted the null hypothesis of no autocorrelation up to order 20for standardized residuals and standardized squared residuals over all theselected countries, which supports the speci?cation of each model.  Tables13 describes  the sample cross-correlations(during  pre-Brexit period) of thestandardized residuals and standardized squared residuals. Evidently thestatistical significance of the cross-correlation of the standardized residualsand that of the squares of  standardizedresiduals  imply there is evidence ofcausality in mean  and variancerespectively. As per the results obtained, it is clear that there is a closerelationship in mean between the stock market in UK and the stock markets inselected developing countries in Asia.

Moreover, feedback dependency in meanhas been observed with India and China with respect to UK. However, no feedbackhas been found for Russia and Japan. Further causality in variance has beenfound for all the selected Asian countries except Russia.  It is to be noted that for causality invariance, feedback also has been found for India and China as like as causalityin mean. Thus, it can be concluded that before Brexit, there is a dynamiclinkage (in mean as well as in variance) between the UK and the selected developingcountries in Asia. Table -12 : Results of empirical analysis of the AR–EGARCHmodels  before Brexit  period.               (February  23,2016 to  June 23,2016)   UK China Russia Japan India Model AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) Mean Equation a0 0.0004 (0.

0002) 0.0015 (0.0003) ** 0.0017 (0.0004) ** 0.0018 (0.0006) ** 0.0013 (0.

0002) ** a1 – 0.0646 (0.0336) 0.

0455 (0.0349) 0.0478 (0.

0358) 0.0462 (0.0366) 0.0489 (0.0358) Variance Equation ? -0.3336 (0.0813) ** -0.3324 (0.

1224)** -0.8125 (0.1523) **   -0.5789 (0.

2237)**   – 1.11561 (0.2556) **   ?1 0.2191 (0.0374) **   0.1713 (0.0458) ** 0.2223 (0.

0482) ** 0.2683 (0.0412) ** 0.

2512 (0.0541) ** ?1 -0.1475 (0.

0311) ** -0.0422 (0.0246) ** -0.2087 (0.0352) ** -0.1268 (0.

0313) ** -0.1656 (0.0389) ** ?1 0.8765 (0.0281) ** 0.9762 (0.

0261) ** 0.8555 (0.0283) ** 0.9785 (0.0261) ** 0.8995 (0.0291) ** GED parameter 1.

4429 (0.0905)** 1.5479 (0.0907)** 1.4328 (0.0911)** 1.6422 (0.

0955)** 1.4722 (0.0885)** Diagnostic Q(20) 16.429 [0.690] 18.173 [0.536]   12.251 [0.

922]   17.872 [0.571] 19.

385 [0.217]   Q2(20) 13.724 [0.

792] 26.028 [0.209] 11.278 [0.944]   8.575 [0.956]   16.

708 [0.706]   Data Source:http://?nance.yahoo.com/                                                                  Result: Computed using E-Views.                                                                                            ** Statistical signi?cance at 0.

01 level of significance.                                          Note: The figures in ()  and []represent  standard errors &  p -values respectively. Q(20) symbolicallyindicates Ljung–Box Q statistic.     Table -13: Teststatistics for causality-in-mean and variance before Brexit  period. (February  23, 2016 to  June 23,2016) M1 (causality-in-mean)   M2 (causality-in-variance)   India -> UK 13.

9222** UK -> India 11.9239** India -> UK 19.7732** UK -> India 23.6739** Japan -> UK 0.9239 UK -> Japan 22.4536** Japan -> UK 0.9239 UK -> Japan 17.

8731** Russia -> UK 0.7201 UK -> Russia 17.9288** Russia -> UK 0.9239 UK -> Russia 0.9239 China -> UK 18.9554** UK -> China 27.7769** China -> UK 20.8736** UK -> China 21.

9999** Data Source:http://?nance.yahoo.com/                                                                  Result: Computed using E-Views.                                                                                            ** Statistical signi?cance at 0.01 level of significance.

 Results of table 11 and table 12 can be represented,in a logical block diagram in figure-1 and in figure-2  as follows. Japan   India   Japan   India                                                                                                                                                                                                                                                                     China   Russia   China   Russia                                                                                                                            Figure-1 :  Logical Block Diagram               Figure-2 :  Logical Block Diagram                                                                                                                                         for Causality in Mean (pre-Brexit)            for Causality in Variance(pre-Brexit)       For post-Brexit, the same type of analysis has been done and table 14and table 15 have been found. Results of table 14 and table 15can be represented, in a logical block diagram in figure-3 and in figure-4  as follows. Japan   India   Japan   India                                                                                                                                                                                                                                                                          UK      China   Russia   China   Russia                                                                                                                            Figure-3 :  Logical Block Diagram               Figure-4 :  Logical Block Diagram                                                                                                                                         for Causality in Mean (post-Brexit)            for Causality in Variance(post-Brexit) Table -14 : Results of empirical analysis of the AR–EGARCHmodels  after  Brexit period.               (March 30, 2017 to  September 29,2017)                           UK China Russia Japan India Model AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) AR(1)-EGARCH(1,1) Mean Equation a0 0.0014 (0.0007) 0.0013 (0.

0004) ** 0.0013 (0.0005) ** 0.0012 (0.0003) ** 0.0011 (0.0008) ** a1 – 0.

0546 (0.0326) 0.0475 (0.

0339) 0.0422 (0.0353) 0.

0461 (0.0375) 0.0535 (0.0351) Variance Equation ? -0.3831 (0.0711) ** -0.3374 (0.

1204)** -0.8421 (0.1123) **   -0.5319 (0.2230)**   – 1.1562 (0.

2552) **   ?1 0.2181 (0.0365) **   0.1793 (0.0471) ** 0.2723 (0.0412) ** 0.

2613 (0.0433) ** 0.1517 (0.0581) ** ?1 -0.1445 (0.0316) ** -0.0472 (0.

0206) ** -0.2067 (0.0358) ** -0.1238 (0.

0817) ** -0.1336 (0.0341) ** ?1 0.

8705 (0.0381) ** 0.9062 (0.0267) ** 0.

8512 (0.0263) ** 0.9005 (0.0265) ** 0.8325 (0.0294) ** GED parameter 1.

4489 (0.0985)** 1.5779 (0.

0903)** 1.4558 (0.0917)** 1.6523 (0.0935)** 1.4121 (0.0885)** Diagnostic Q(20) 17.425 [0.

690] 16.178 [0.536]   15.259 [0.922]   16.

874 [0.571] 18.665 [0.217]   Q2(20) 14.724 [0.

592] 16.028 [0.609] 13.

988 [0.844]   18.599 [0.946]   15.798 [0.636]   Data Source:http://?nance.

yahoo.com/                                                                  Result: Computed using E-Views.                                                                                            ** Statistical signi?cance at 0.01 level of significance.                                          Note: The figures in ()  and []represent  standard errors &  p -values respectively.

Q(20) symbolicallyindicates Ljung–Box Q statistic.  Table -15: Teststatistics for causality-in-mean and variance after Brexit  period. (March 30, 2017 to September 29,2017) M1 (causality-in-mean)   M2 (causality-in-variance)   India -> UK 0.5274 UK -> India 0.7254 India -> UK 0.

5232 UK -> India 0.6537 Japan -> UK 0.9559 UK -> Japan 0.

4226 Japan -> UK 0.9239 UK -> Japan 15.2571** Russia -> UK 0.6204 UK -> Russia 0.8213 Russia -> UK 0.

4259 UK -> Russia 0.9255 China -> UK 16.8854** UK -> China 0.7551 China -> UK 0.

5126 UK -> China 0.9849 Data Source:http://?nance.yahoo.com/                                                                  Result: Computed using E-Views.                                                                                            ** Statistical signi?cance at 0.01 level of significance.

 Thus remarkable difference has beenfound in pre-Brexit and post-Brexit periods. Hence it can be concluded thatBrexit definite has a high impact on stock markets in Asia. Morespecifically,  this paper shows theenough evidence that Brexit made the dynamic linkages among selected stockmarkets weak by eliminating the causality relations in mean and in variance (asevident from figure 1, figure 2, figure 3 and figure 4).     5.

ConclusionAfter verifying theinfluence of Brexit on selected stock markets, the present paper uses  the test developed by Hong (2001) toinvestigate the causal relationships of stock markets  in mean and variance between the selecteddeveloping Asian countries  and theUnited Kingdom. In particular, the paper focused on the impact of  Brexit, on the short term dynamic linkagesbetween the stock prices of the selected countries. Our empirical resultsindicated that the international transmission of stock prices between theselected developing countries in Asia and the United Kingdom  signi?cantly weakened in both the mean andvariance after the event of Brexit. This findings definitely  will change in both retail investors as wellas institutional investors  behavior dueto  the happening of Brexit and provideguidance to them for managing  portfoliodiversification over different stock markets in the world.

The findings of thispaper may shift funds gradually from stock markets to other financial marketssuch as commodities market or gold market in the post-Brexit period.

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