Project Title: To Analyze Relationships and Trends of Stock Prices in Amsterdam, Frankfurt, London, Hong Kong, Japan, Singapore and New York
Tools: R-Programming for advanced statistics and Microsoft Excel
In our data analysis, to start with linear regression, the following linear model equations for the seven stock markets are as follows:
x.Amsterdam=0.1541 t +127.2803 x.Frankfurt=0.6327 t + 897.7938
x.London =0.9158 t + 1304.6411 x.HongKong=3.975 t -103.148
x.Japan=-2.322 t + 26004.867 x.Singapore =0.1031 t + 253.0322
x.NewYork=0.1809 t + 153.5884
The analysis of correlation of the stock prices between the seven markets
We want to determine whether the relationship of the variations in these markets.
The following is the correlation Matrix.
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According to the above correlation analysis, it is conspicuously notable that all stock prices for Japan are negatively correlated to the rest of stock prices in all other markets. The stock prices in Amsterdam and Frankfurt has the highest positive correlation of 0.99.
One Sample t-test Analysis
Statement of hypotheses (For a two-tailed test):
Ho: True mean =0
H1: True mean ≠0
In our hypothesis test, the p-value for all prices in the seven markets in less than 2.2*10-16. Testing at 5% significance level, we reject the null hypothesis in favour of the alternative. Thus the true mean for all the stock prices in the seven markets is not equal to zero.
The confidence interval of the tocks prices in the seven markets is as follows:
362.3519<x.Amsterdam<374.4171 , 1863.285 <x.Frankfurt<1911.902
, 2706.484<x.London<2768.353, 5981.009<x.HongKong<6251.341
, 22175.58 <x.Japan<22568.98 , 410.6102 <x.Singapore<418.1576
, 430.2920 <x.Singapore<442.9017
F-test for variance ratios
Hypotheses statement:
Ho: True variance ratio =1
H1: True variance ratio ≠1
The p-value for the two-tailed f-test for the variance ration between the stock prices in all the seven markets is always less than 2.2*10-16. Therefore we reject the null hypothesis and conclude that the true variance ratio is never equal to one, at 5% significance level.
Welch Two Sample t-test
Hypothesis statement:
Ho: True difference in means is not equal =0
H1: True difference in means is not equal ≠0
The p-value in the Welch two sample two-tailed t-test, for the difference of means is always less than 2.2*10-16. Thus, testing at 95% confidence interval we reject the null hypothesis and conclude that the true difference in the mean of stock prices in all seven markets in not equal to zero.
ANOVA
Combined ANOVA Table For all Time series data
Independence test between Stock prices in Amsterdam and Frankfurt
Ho: Stock prices in Amsterdam and Frankfurt are independent
H1: Stock prices in Amsterdam and Frankfurt are related
Using the Pearson's Chi-squared test, to investigate the independence between Stock prices in Amsterdam and Frankfurt, since these markets are geographically near, the p-value of the test is less than 2.2*10-16. Thus we reject the null hypothesis in favour of the alternative hypothesis, and conclude that the stock prices in these two markets are generically dependent.
References
R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Retrieved on 7th August 2013 from
http://www.R-project.org/
Source of data:
Massey University (2012). Stock market data. Retrieved on 1st February 2013 from http://www.massey.ac.nz/~pscowper/ts/stockmarket.dat
