1. Lea-‐Marie
Lamm
The
report
illustrates
the
relationship
between
the
American
and
Australian
stock
market
based
on
quarterly
and
daily
data
of
the
Australian-‐US
dollar
exchange
rate,
the
Dow-‐Jones
Industrial
Index
(DJ)
and
the
Australian
All
Ordinaries
Index
(ASX).
The
following
analysis
concluded
that
the
ASX
has
a
positive
effect
on
the
DJ
by
approximately
30%.
Additionally,
the
volatility
of
both
markets
indicates
a
connection.
E C O N
1 1 9 5
–
F i n a n c i a l
E c o n o m e t r i c s
m
The
Relationship
between
the
United
States
and
Australian
Stock
Markets
3481019
3. 2
Introduction
The given data has three components - year, price index and exchange rate ratio –
and is based on quarterly data over the past 30 years and daily data over the past
five years. The year is an independent or explanatory variable while price index is a
dependent variable. The DJ is a ratio that depends on the price-weighted average of
30 mostly traded blue-chip stocks. Therefore, it is dependent on the price variation of
the active stocks. As already mentioned, the year is an independent variable since it
is not affected by any market fluctuation. Further, the ASX is the index of all common
shares from the Australian stock exchange. It depends on the number of companies
trading on the market and their stock prices.
Additionally, it can be seen that three major financial events had an impact on the
data. The ‘Black Monday’ (October 1987), the all-time high of the gasoline prices
(May 2008), and the massive drop of the Dow Jones Industrial Average (March
2009) effected the indices in America and worldwide.
In the following I will explain the relationship between the United States and
Australian stock market and the effect of volatility in these markets. To conduct the
results I obtained the models and done the testing in eviews. All outputs and tests
are shown in the appendix.
Analysis
The evaluation shows that there exists a close relationship between Australian and
US stock markets. The dependent variable in the US and Australian market is the
price of the stocks. Moreover, the generated multivariate generalized autoregressive
model is useful in explaining the relationship between the two markets. The
estimated model identifies that the negative shocks play a critical role in increasing
the variances across the market and in addition, the volatility in the Australian market
increases due to negative shocks from larger markets like the US. However, with the
use of dummy variables I was able to eliminate the negative effects. Ones can say
that the relationship between the stock market and its growth is due to volatility
across the two markets (Dufrénot, Jawadi & Louhichi, 2014, p. 120).
4. 3
The regression analysis as shown in the appendix shows the relationship between
the two markets.
Dlog(ASX) = 0.01489 + 0.3128 Dlog(DJAUS) - 0.2993DV + 0.4771𝐷𝑉! - 0.4694 𝐷𝑉!"
In addition, a covariance model is recommended to capture timing and effects on the
volatility of the two markets. It is obvious that there is an influence arising from
inherent volatility of the markets. The nature of the relationship is the interaction
volatility effect. Furthermore, spillover effects due to market volatility have a direct
impact on the markets.
As the model illustrates, the US stock market influences the Australian stock market,
which can be explained by the fact that the US economy affects the Australian
economic growth. The volatility shocks between the stock markets and GDP is
positive. There are asymmetric volatility effects in between and across the markets
(Dufrénot, Jawadi & Louhichi, 2014, p. 124).
The individual regression analysis for each market is an indicator of whether the
market is volatile or not.
Australian Market: Dlog (ASX) = 9.58E-05 – 0.0826Dlog(DJAUS)
US market: Dlog (DJAUS) = 0.00056 – 0.1351Dlog(ASX)
Conclusion
The preceding analysis showed that a positive relationship between the US and
Australian stock market exists and that, due to the fact that the American market is
by far bigger, changes there impact the market on the other side of the world as well.
America is the leading country in the world and whatever happens in the United
States has an impact on the world economies as previous events showed (e.g.
housing bubble in 2007).
5. 4
Reference List
Crisan, D., Hambly, B. M., Zariphopoulou, T., & Lyons, T. J. (2014). Stochastic
analysis and applications 2014: in honour of Terry Lyons.
Dufrénot, G., Jawadi, F., & Louhichi, W. (2014). Market microstructure and nonlinear
dynamics keeping financial crisis in context. Cham, Springer.
International Conference on Economics and Management Engineering. (2014). 2014
International Conference on Economics and Management Engineering (ICEME
2014) proceedings. Lancaster, PA, DEStech Publications, Inc.
6. 5
Appendix
Question 1:
a) Since I am working with financial time series data, it is not possible to use the
raw data set. To decide whether or not to use logged data or difference
logged data I had a look at the line graph. As can be seen in figure 1 there is
no cointegration between the logged data of the DJAUS, which I converted
into Australian Dollar (DJAUS), and the ASX. Therefore, there will be no
short-run equation and for further testing the long-run equation is used.
Figure 1
I will use ASX as my dependent variable and DJ as my independent variable,
because I believe that changes in the DJ will have a bigger impact on the ASX than
vice versa. Moreover, I will include three event dummy variables (DV) as the
residuals showed spikes at Q4 1987, Q2 2008 and Q1 2009. Graph 2 shows the
residuals after including the DV.
5
6
7
8
9
10
11
86 88 90 92 94 96 98 00 02 04 06 08 10 12 14
Log DJAUS Log ASX
7. 6
Figure 2
b) My mean equation is showed below and the correlogram below shows no
autocorrelation and therefore, no more adjustments have to be made.
Dependent Variable: DLOG(ASX)
Method: Least Squares
Date: 11/06/15 Time: 17:49
Sample (adjusted): 1985Q4 2015Q3
Included observations: 120 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
DLOG(DJAUS) 0.312806 0.080650 3.878566 0.0002
DV -0.299291 0.062239 -4.808709 0.0000
DV9 0.477166 0.087403 5.459363 0.0000
DV87 -0.469401 0.066248 -7.085535 0.0000
C 0.014890 0.006034 2.467641 0.0151
R-squared 0.528499 Mean dependent var 0.016447
Adjusted R-squared 0.512099 S.D. dependent var 0.088480
S.E. of regression 0.061803 Akaike info criterion -2.688945
Sum squared resid 0.439260 Schwarz criterion -2.572800
Log likelihood 166.3367 Hannan-Quinn criter. -2.641778
F-statistic 32.22552 Durbin-Watson stat 1.968544
Prob(F-statistic) 0.000000
-.2
-.1
.0
.1
.2
-.6
-.4
-.2
.0
.2
86 88 90 92 94 96 98 00 02 04 06 08 10 12 14
Residual Actual Fitted
9. 8
H0: The errors are normally distributed.
H1: The errors are not normally distributed.
Level of significance: α=0.05
Test statistic: Jarque-Bera Test
P-Value: 0.924
Conclusion: Do not reject H0 the errors are normally distributed.
Heteroskedasticity:
H0: The variance of errors is constant and therefore, the errors are homoskedastic.
H1: The variance of errors is not constant and thus, the errors are heteroskedastic.
Level of significance: α=0.05
Test statistic: White test
P-value: 0.8395
Conclusion: Do not reject null. The errors are homoscedastic.
Heteroskedasticity Test: White
F-statistic 0.412180 Prob. F(5,114) 0.8395
Obs*R-squared 2.130847 Prob. Chi-Square(5) 0.8308
Scaled explained SS 1.821386 Prob. Chi-Square(5) 0.8733
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/07/15 Time: 11:38
Sample: 1985Q4 2015Q3
Included observations: 120
Collinear test regressors dropped from specification
Variable Coefficient Std. Error t-Statistic Prob.
C 0.003561 0.000594 5.999956 0.0000
DLOG(DJAUS)^2 0.038975 0.058744 0.663475 0.5084
DLOG(DJAUS)*DV 0.109152 0.153556 0.710825 0.4786
DLOG(DJAUS)*DV9 0.006989 0.222613 0.031395 0.9750
DLOG(DJAUS)*DV87 0.024840 0.025159 0.987332 0.3256
DLOG(DJAUS) -0.001050 0.006628 -0.158432 0.8744
R-squared 0.017757 Mean dependent var 0.003660
Adjusted R-squared -0.025324 S.D. dependent var 0.005015
S.E. of regression 0.005078 Akaike info criterion -7.679007
Sum squared resid 0.002940 Schwarz criterion -7.539632
Log likelihood 466.7404 Hannan-Quinn criter. -7.622406
F-statistic 0.412180 Durbin-Watson stat 1.925804
Prob(F-statistic) 0.839490
10. 9
Augmented Dickey-Fuller:
H0: The ASX contains stochastic trend (has a unit root).
H1: The ASX only contains a deterministic trend.
Level of significance: α=0.05
Test statistic: ADF at levels with no trend and intercept and 12 lags selected by AIC.
P-Value: 0.3061
Conclusion: Do not reject H0; the ASX follows a stochastic trend process.
Null Hypothesis: ASX has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 0 (Automatic - based on AIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.545589 0.3061
Test critical values: 1% level -4.036310
5% level -3.447699
10% level -3.148946
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ASX)
Method: Least Squares
Date: 11/07/15 Time: 12:48
Sample (adjusted): 1985Q4 2015Q3
Included observations: 120 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
ASX(-1) -0.110908 0.043569 -2.545589 0.0122
C 36.24547 17.73813 2.043364 0.0433
@TREND("1985Q3") 1.480852 0.654279 2.263334 0.0255
R-squared 0.053394 Mean dependent var 11.82967
Adjusted R-squared 0.037212 S.D. dependent var 88.61761
S.E. of regression 86.95314 Akaike info criterion 11.79330
Sum squared resid 884619.3 Schwarz criterion 11.86299
Log likelihood -704.5979 Hannan-Quinn criter. 11.82160
F-statistic 3.299715 Durbin-Watson stat 1.789088
Prob(F-statistic) 0.040356
11. 10
Null Hypothesis: DJAUS has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 7 (Automatic - based on AIC, maxlag=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -2.253592 0.4553
Test critical values: 1% level -4.041280
5% level -3.450073
10% level -3.150336
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DJAUS)
Method: Least Squares
Date: 11/09/15 Time: 14:35
Sample (adjusted): 1987Q3 2015Q3
Included observations: 113 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
DJAUS(-1) -0.052040 0.023092 -2.253592 0.0263
D(DJAUS(-1)) 0.203659 0.094214 2.161679 0.0330
D(DJAUS(-2)) -0.065984 0.091052 -0.724682 0.4703
D(DJAUS(-3)) 0.230248 0.093233 2.469587 0.0152
D(DJAUS(-4)) 0.105410 0.097098 1.085609 0.2802
D(DJAUS(-5)) 0.014515 0.095942 0.151294 0.8800
D(DJAUS(-6)) 0.399076 0.095718 4.169308 0.0001
D(DJAUS(-7)) -0.153976 0.103115 -1.493238 0.1384
C 127.1468 172.3570 0.737695 0.4624
@TREND("1985Q3") 8.222103 3.763633 2.184619 0.0312
R-squared 0.280164 Mean dependent var 176.9478
Adjusted R-squared 0.217266 S.D. dependent var 879.4725
S.E. of regression 778.0890 Akaike info criterion 16.23589
Sum squared resid 62358519 Schwarz criterion 16.47725
Log likelihood -907.3279 Hannan-Quinn criter. 16.33383
F-statistic 4.454249 Durbin-Watson stat 2.015038
Prob(F-statistic) 0.000060
H0: The DJAUS contains stochastic trend (has a unit root).
H1: The DJAUS only contains a deterministic trend.
Level of significance: α=0.05
Test statistic: ADF at levels with no trend and intercept and 12 lags selected by AIC.
P-Value: 0.4553
Conclusion: Do not reject H0; the DJAUS follows a stochastic trend process.
12. 11
Variance Inflation Test:
Due to the fact, that the centered VIF is less than the critical value of 10, there is no
multicollinearity.
c) The chosen model shows that there is positive correlation between ASX and
DJAUS. Meaning if DJAUS changes by one per cent, there will be a 31.28%
change in ASX. In addition, the event DV’s estimated coefficients show the
change in the intercept. For example, DV9 indicates the change in the
intercept in Q1 2009 by 47.72%. Moreover, the R-squared value shows that
about 52% of the variation can be explained by the chosen model. Based on
the fact that all errors were already fixed by DVs, all conducted tests follow
the expirations of showing no errors in the model.
Variance Inflation Factors
Date: 11/08/15 Time: 14:50
Sample: 1985Q3 2015Q3
Included observations: 120
Coefficient Uncentered Centered
Variable Variance VIF VIF
DLOG(DJAUS) 0.006504 1.236724 1.149005
DV 0.003874 2.028314 1.994509
DV9 0.007639 2.000007 1.983341
DV87 0.004389 1.148999 1.139424
C 3.64E-05 1.143850 NA
13. 12
Question 2:
The correlogram of squared residuals is shown above. Clearly there are ARCH effects. It
now makes sense to fit an Ma(1) process. The output is given below. Therefore, I fit a
GARCH(1,1) model to satisfy the requirements for a stable variance process.
14. 13
Dependent Variable: DLOG(DJAUS)
Method: Least Squares
Date: 11/08/15 Time: 18:51
Sample (adjusted): 9/16/2010 9/15/2015
Included observations: 1304 after adjustments
Convergence achieved after 5 iterations
MA Backcast: 9/15/2010
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000556 0.000212 2.621059 0.0089
MA(1) -0.261595 0.026751 -9.779020 0.0000
R-squared 0.063508 Mean dependent var 0.000558
Adjusted R-squared 0.062789 S.D. dependent var 0.010707
S.E. of regression 0.010365 Akaike info criterion -6.299218
Sum squared resid 0.139880 Schwarz criterion -6.291284
Log likelihood 4109.090 Hannan-Quinn criter. -6.296242
F-statistic 88.29521 Durbin-Watson stat 1.997137
Prob(F-statistic) 0.000000
Inverted MA Roots .26
15. 14
H0: There are no ARCH effects.
H1: The series contains ARCH effects.
Level of significance: α= 0.05
Test statistic: LM test for ARCH
P-Value: 0.0000
Conclusion: Reject H0; the series contains ARCH effects.
Heteroskedasticity Test: ARCH
F-statistic 164.8653 Prob. F(1,1301) 0.0000
Obs*R-squared 146.5479 Prob. Chi-Square(1) 0.0000
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 11/08/15 Time: 20:00
Sample (adjusted): 9/17/2010 9/15/2015
Included observations: 1303 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 7.13E-05 6.16E-06 11.58611 0.0000
RESID^2(-1) 0.335360 0.026118 12.83999 0.0000
R-squared 0.112470 Mean dependent var 0.000107
Adjusted R-squared 0.111787 S.D. dependent var 0.000210
S.E. of regression 0.000198 Akaike info criterion -14.21615
Sum squared resid 5.09E-05 Schwarz criterion -14.20821
Log likelihood 9263.821 Hannan-Quinn criter. -14.21317
F-statistic 164.8653 Durbin-Watson stat 2.090856
Prob(F-statistic) 0.000000
16. 15
Figure
3
GARCH(1,1)
Dependent Variable: DLOG(DJAUS)
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 11/08/15 Time: 20:08
Sample (adjusted): 9/16/2010 9/15/2015
Included observations: 1304 after adjustments
Convergence achieved after 10 iterations
MA Backcast: 9/15/2010
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 0.000635 0.000195 3.250161 0.0012
MA(1) -0.229277 0.028294 -8.103475 0.0000
Variance Equation
C 3.40E-06 1.16E-06 2.940318 0.0033
RESID(-1)^2 0.085291 0.014154 6.026008 0.0000
GARCH(-1) 0.881425 0.021513 40.97232 0.0000
R-squared 0.062427 Mean dependent var 0.000558
Adjusted R-squared 0.061707 S.D. dependent var 0.010707
S.E. of regression 0.010371 Akaike info criterion -6.455184
Sum squared resid 0.140041 Schwarz criterion -6.435348
Log likelihood 4213.780 Hannan-Quinn criter. -6.447743
Durbin-Watson stat 2.060859
Inverted MA Roots .23
17. 16
Check for threshold:
The threshold is not needed and hence, I will use the before estimated
GARCH(1,1) model.
Static forecast:
Dependent Variable: DLOG(DJAUS)
Method: ML - ARCH (Marquardt) - Normal distribution
Date: 11/08/15 Time: 20:11
Sample (adjusted): 9/16/2010 9/15/2015
Included observations: 1304 after adjustments
Convergence achieved after 12 iterations
MA Backcast: 9/15/2010
Presample variance: backcast (parameter = 0.7)
GARCH = C(3) + C(4)*RESID(-1)^2 + C(5)*RESID(-1)^2*(RESID(-1)<0) +
C(6)*GARCH(-1)
Variable Coefficient Std. Error z-Statistic Prob.
C 0.000490 0.000195 2.514071 0.0119
MA(1) -0.225485 0.029335 -7.686554 0.0000
Variance Equation
C 4.89E-06 1.31E-06 3.744208 0.0002
RESID(-1)^2 0.037644 0.018289 2.058321 0.0396
RESID(-1)^2*(RESID(-1)<... 0.109736 0.028741 3.818137 0.0001
GARCH(-1) 0.859452 0.025258 34.02698 0.0000
R-squared 0.062210 Mean dependent var 0.000558
Adjusted R-squared 0.061490 S.D. dependent var 0.010707
S.E. of regression 0.010372 Akaike info criterion -6.465845
Sum squared resid 0.140074 Schwarz criterion -6.442042
Log likelihood 4221.731 Hannan-Quinn criter. -6.456915
Durbin-Watson stat 2.068362
Inverted MA Roots .23
Dependent Variable: DLOG(ASX)
Method: Least Squares
Date: 11/08/15 Time: 20:20
Sample (adjusted): 9/20/2010 9/15/2015
Included observations: 1302 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
DLOG(VOLATILITY) -0.003992 0.002042 -1.954621 0.0508
C 5.39E-05 0.000232 0.232686 0.8160
DLOG(VOLATILITY(-1)... 0.002565 0.002043 1.255631 0.2095
R-squared 0.004075 Mean dependent var 5.28E-05
Adjusted R-squared 0.002542 S.D. dependent var 0.008369
S.E. of regression 0.008358 Akaike info criterion -6.728859
Sum squared resid 0.090746 Schwarz criterion -6.716942
Log likelihood 4383.487 Hannan-Quinn criter. -6.724388
F-statistic 2.657632 Durbin-Watson stat 1.957834
Prob(F-statistic) 0.070495
