Research Methodology in Finance: Stock Market Analysis, GRA 65476

This assignment presents a comprehensive analysis of stock market indices using various statistical and econometric techniques. The first part focuses on analyzing the S&P500, DAX30, and Nikkei225 indices, including data import, stationarity tests, lead-lag relationships using multivariate regression and Granger causality, impulse response functions, and variance decomposition. The second part examines the relationship between dividends and earnings using a partial adjustment model, time series plots, and co-integration tests. The analysis involves the use of MATLAB for data processing and statistical modeling, providing detailed results, interpretations, and references to relevant literature. The assignment explores key concepts such as stationarity, Granger causality, VAR modeling, and co-integration to understand the dynamics and interdependencies within the financial markets.

Statistics
Research Methodology in Finance
Student Name –
Student ID -
Solution 1)
Initially, the data is downloaded from Yahoo Finance for the 3 stock market indices for a
period of time. The 3 stock markets selected are : S&P500, DAX30 and Nikkei225. The data
is then imported into the software MATLAB. The column considered is the adjusted closing
price for every index and the other variables are not considered. This is because we are
mainly interested in the adjusted closing price. There are 3 csv files containing the data. The
files are : sp.csv ( for S&P500 ), dx.csv ( for DAX30 ) and nk.csv ( for Nikkei225 ). The data
containing the adjusted closing price for every index is store in column vectors named s, d,
and n respectively.
The merged data is obtained. The starting point is made the same for all the 3 time series. The
sample period is chosen as 1 day. The sample period ends at 28th February 2020. A uniform
data is obtained for all the 3 cases. The data is now ready for analysis.

a) The sample period which we have chosen has 20 th March 2019 as the first
observation date. The total number of observations is 239 for all the 3 cases under
consideration.
The adjusted closing prices are then plotted for all the 3 cases one by one using Matlab plot
command. On the basis of the plots obtained , it can be seen that the price time series of the 3
stock markets , S&P500, DAX30 and Nikkei225 – are not stationary. The mean, variance and
the autocorrelation are not constant with time. The data has upward as well as the downward
trends as well as seasonal effects ( Box, 2015 ).
In the next step, the log returns are computed for each stock index and the sample period is
adjusted accordingly. The plot for all the 3 time series is obtained. These plots show that
S&P500 and Nikkei225 are stationary and DAX30 is not stationary. The mean, variance and
the autocorrelation for S&P500 and Nikkei225 are constant with time. The data does not have
upward as well as the downward trends as well as seasonal effects ( Charfeddine, 2016 ). The
mean, variance and the autocorrelation for DAX30 are not constant with time. The data has
upward as well as the downward trends as well as seasonal effects doe DAX30.
Next, all the 3 log return time series are tested for stationarity. The values are reported for 5
% significance level. The p – values have been found using Matlab.
The p values obtained are :
p = 1.7533e-11
p = 2.9858e-15

p = 0.2903
It can be seen that the p values obtained here are very small. There is a very big evidence that
the alternative hypothesis must be favoured ( Dritsaki, 2014 ).
b) In this step, the lead – lag relation is studied between the log returns of the 3 stock
market indices. A method for analysis suggested is by the use of multivariate
regression ( Dufrénot, 2012 ). By using the multivariate time series, it becomes very
easy in identifying any change in the structure of relation between the variables.
Suppose there is a structural change in a spot index and using a system which is
bivariate ( 2 variables ) it is shown that the futures price has changed ( Wen, 2019 ).
It can be seen that the spot market is leading the futures market. A similar result can
be derived vice versa also. The clusters are also found which show common
behaviour in the bivariate system and the spot index. If it is assumed that a system is
represented using a multivariate time series, then the system can be realised. Here,
some terms are used like individuals ( participants in the competition ), population
( collection of all the individuals ), activity function ( deciding success or failure of an
individual ) and the learning process for the system ( Xu, 2014 ).
Genetic algorithm can be used to implement the multi variate regression analysis. It
can help in detecting any structural changes in the multi variate time series. If
multivariate analysis is used in probabilistic theory, then good models can be
designed.

c) A two-dimensional VAR using the log returns of the S&P500 and the Nikkei225 has
been set up. Based on the Hannan-Quinn criterion, the optimal lag length for up to six
lags has been determined. The parameter estimates and their t-statistics, and the
adjusted R2values are reported based on a 5% significance level. If there is a positive
two-standard deviation shock to the log return of the S&P500 (or the log return of the
Nikkei225, respectively), then the log return of the Nikkei225 (or the log return of the
S&P500, respectively) react in a similar fashion. This shows that the economies of
both the stock markets indices are related.
Results :
h1 = 0
pValue1 = 0.8734
stat1 = -1.1384
cValue1 = -3.3629
reg11 =
num: 239
size: 239
names: {2x1 cell}
coeff: [2x1 double]
se: [2x1 double]
Cov: [2x2 double]

tStats: [1x1 struct]
FStat: [1x1 struct]
yMu: 3.0203e+03
ySigma: 157.4392
yHat: [239x1 double]
res: [239x1 double]
DWStat: 0.0540
SSR: 2.2707e+06
SSE: 3.6287e+06
SST: 5.8993e+06
MSE: 1.5311e+04
RMSE: 123.7370
RSq: 0.3849
aRSq: 0.3823
LL: -1.4897e+03
AIC: 2.9833e+03
BIC: 2.9903e+03
HQC: 2.9861e+03
reg21 =

num: 239
size: 238
names: {'a'}
coeff: 0.9826
se: 0.0152
Cov: 2.3230e-04
tStats: [1x1 struct]
FStat: [1x1 struct]
yMu: 0.5311
ySigma: 123.4631
yHat: [238x1 double]
res: [238x1 double]
autoCov: 'PP tests only'
NWEst: 'PP tests only'
DWStat: 1.9889
SSR: 3.4182e+06
SSE: 1.9488e+05
SST: 3.6131e+06
MSE: 822.2598

RMSE: 28.6751
RSq: 0.9461
aRSq: 0.9461
LL: -1.1359e+03
AIC: 2.2739e+03
BIC: 2.2774e+03
HQC: 2.2753e+03
d)
For studying the relation between the S&P500 and the Nikkei225, Granger causality tests
have been performed on the log returns of both indices based on the results.
Suppose that the null hypothesis says H0 : s = n.
Then the alternative hypothesis is s is not equal to n.
Results :
Result is h = 1
If the returned value is h = 1 then it shows that ttest rejects the null hypothesis at the 5%
significance level.
e) In the next step, the relation between the S&P500 and the Nikkei225 is studied using
impulse response functions based on previous results.
Results :

The result shows that an impulse of rise in one triggers a fall in the other and vice versa. This
is very important as far as the market is concerned as a fall of one may lead to the rise of the
other one.
0 50 100 150 200 250
2000
3000
4000
5000
6000
7000
8000
9000
S&P500
Nikkei225
Figure 1
f) A variance decomposition is performed next.

0 50 100 150 200 250
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
S&P500
Nikkei225
Figure 2
The results show that the rise in S&P500’s value shows a fall in Nikkei225’s value. There is
an inverse relation between both.
g) Finally, we want to study the lead-lag relation between the DAX30 and the S&P500 in a
VAR(2). The previous exercises are repeated for them. The results are shown below.
h = 1

If the returned value is h = 1 then it shows that ttest rejects the null hypothesis at the 5%
significance level. Hence, as the value obtained for ‘h’ is 1 here, it shows that the null
hypothesis can be rejected at the 5% significance level.
0 50 100 150 200 250
0
500
1000
1500
2000
2500
3000
3500
S&P500
DAX30
Figure 3

0 50 100 150 200 250
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
S&P500
DAX30
Figure 4
The above figure shows that as the values increase for S&P500, the values for DAX30 also rise and
vice versa. The levels may not be same throughout but the rise and fall are similar in pattern.
Solution 2)
The dataset used has been stored as ‘abc.xls’. The dataset is obtained from the Robert
Shiller’s homepage. The data contains the monthly U.S. stock market data from Januaery
1871 to December 2019.
The major focus has been laid on the time series of dividends (D) and the earnings (E). The
partial adjustment model has been used to describe the relation between the dividends and
earnings.

The long run relation is studied between the dividends and the earnings. The following graph
shows the plot for both the dividends and the earnings on the same graph.
0 500 1000 1500 2000 2500
-2
-1
0
1
2
3
4
5
Figure 5
It can be clearly seen that there is a strong relation between the dividends and the earnings.
Now, the log transformations of both the time series are studied.
The plot for Dividend obtained is :