4.5 Autoregressive models: Such models like autoregressive (AR) model and the
exponential generalized autoregressive conditional heteroskedasticity (EGARCH)
model are useful to test the impact of Brexit on the dynamic linkages and
causal relationships among the selected stock markets.
Table
12 depicts the results of the empirical
analysis with AR(1)–EGARCH(1,1) models
during pre-Brexit period. All the
coef?cients of the EGARCH term (?) , all
coefficients of asymmetric effects (?)
and GED parameter estimates have been
found to be statistically
signi?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 normal
distribution. Evidently it indicates the
existence of ARCH effects. Moreover, this table
indicates the diagnostics statistics of analysis of the AR–EGARCH
models—the Q(s) and the Q 2(s) . The Q statistic at lag s, Q(s), is
a test statistic for the null hypothesis that there is no autocorrelation up to
order s for standardized residuals; it is asymptotically distributed as
chi-square, with the degrees of freedom equal to the number of autocorrelation
less the number of parameters. The Q 2(s) is that for squared residuals . Result of
this paper accepted the null hypothesis of no autocorrelation up to order 20
for standardized residuals and standardized squared residuals over all the
selected countries, which supports the speci?cation of each model.
Tables
13 describes the sample cross-correlations
(during pre-Brexit period) of the
standardized residuals and standardized squared residuals. Evidently the
statistical significance of the cross-correlation of the standardized residuals
and that of the squares of standardized
residuals imply there is evidence of
causality in mean and variance
respectively. As per the results obtained, it is clear that there is a close
relationship in mean between the stock market in UK and the stock markets in
selected developing countries in Asia. Moreover, feedback dependency in mean
has been observed with India and China with respect to UK. However, no feedback
has been found for Russia and Japan. Further causality in variance has been
found for all the selected Asian countries except Russia. It is to be noted that for causality in
variance, feedback also has been found for India and China as like as causality
in mean. Thus, it can be concluded that before Brexit, there is a dynamic
linkage (in mean as well as in variance) between the UK and the selected developing
countries in Asia.
Table -12 : Results of empirical analysis of the AR–EGARCH
models 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:
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) symbolically
indicates Ljung–Box Q statistic.
Table -13: Test
statistics 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:
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 14
and table 15 have been found. Results of table 14 and table 15
can 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–EGARCH
models 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:
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) symbolically
indicates Ljung–Box Q statistic.
Table -15: Test
statistics 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:
Result: Computed using E-Views.
** Statistical signi?cance at 0.01 level of significance.
Thus remarkable difference has been
found in pre-Brexit and post-Brexit periods. Hence it can be concluded that
Brexit definite has a high impact on stock markets in Asia. More
specifically, this paper shows the
enough evidence that Brexit made the dynamic linkages among selected stock
markets weak by eliminating the causality relations in mean and in variance (as
evident from figure 1, figure 2, figure 3 and figure 4).
5.
Conclusion
After verifying the
influence of Brexit on selected stock markets, the present paper uses the test developed by Hong (2001) to
investigate the causal relationships of stock markets in mean and variance between the selected
developing Asian countries and the
United Kingdom. In particular, the paper focused on the impact of Brexit, on the short term dynamic linkages
between the stock prices of the selected countries. Our empirical results
indicated that the international transmission of stock prices between the
selected developing countries in Asia and the United Kingdom signi?cantly weakened in both the mean and
variance after the event of Brexit. This findings definitely will change in both retail investors as well
as institutional investors behavior due
to the happening of Brexit and provide
guidance to them for managing portfolio
diversification over different stock markets in the world. The findings of this
paper may shift funds gradually from stock markets to other financial markets
such as commodities market or gold market in the post-Brexit period.
