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quotes (X2) and Dow-Jones industrial average. If X2 increases by 1$ Y will increase by 11,85 points.
Coefficient a0 is the value of Dow-jones industrial average (Y) in case if a1 and a2 are both equal to 0.
Conclusion. The investigation shows that there is a correlation between Dow-Jones Industrial Average and Google and Apple share quotations though as far as matrix of pair correlation is concerned Apple company weakly correlates with DJIA. And it should not come as surprise because concerning the period the data reflects the DJIA reflecting the general situation in the US stock market may show growth and Google company is one the companies that showed positive dynamic whereas Apple company performed growth slower than the whole stock exchange.
List of references
1.Трегуб А.В., Трегуб И.В. Методика прогнозирования показателей стохастических экономических систем — Вестник Московского государственного университета леса — Лесной вестник. 2008. № 2. С. 144— 151.
2.Трегуб А.В., Трегуб И.В. Методика прогнозирования основных показателей развития отраслей российской экономики — Вестник Московского государственного университета леса - Лесной вестник. 2014. № 4 (103). С. 231—236.
3.Шарп У.Ф., Александер Г.Дж., Бэйли Дж.В. Инвестиции — М.: Инфра — М, 2001.
4. Finam.ru.
Bagdasaryan A. student-bachelor 3d-year student
Financial university under the government of Russian Federation
Russia, Moscow
CONSTRUCTING AND TESTING THE MODEL OF THE US STOCK
MARKET
This work is dedicated to testing the model which reflects the relationship between Dow-jones industrial average and prices of two giant companies Google and Apple. The question is why these companies being the leaders in their fields of economy are not included in the list of companies taken into account to compute DJIA.
The econometric model transformed into math language (specification of the model) is going to be like this:
(Yt = ao+a^t + o^t + et j a12> 0
Initial form
EOt) = 0 a(st) = const
Yt - the Dow-Jones Industrial average, points
X1t-price of one Apple Inc. share, $
X2t -price of one Google Inc. share, $
To estimate this model we need to conduct regression analysis. To do this we apply for the special function in Microsoft. The Excel calculates everything and presents the result in several successive tables. This model is estimated according to data which was taken from http://www.finam.ru/.
Now the coefficients and the whole model should be checked according three basic tests: t-test, ft2-test and F-test. Mind that t statistics for a0 and a1 are also given in the tables of regression analysis (numbers in square brackets in the system)
Interpreting the coefficients of model
Coefficients of regression show how the dependent variable (regressand) of the model will change if the independent variables (regressors) change within the certain model.
Coefficient a1 before X1 (apple shares quotes) means that if Apple Shares quotes for example increase by 1 $ Dow-Jones industrial average (Y) will increase by 14,34 points. This coefficient shows the certain dependence of Y from X1 in point of view math. So does the coefficient a2 but concerning Google shares quotes (X2) and Dow-Jones industrial average. If X2 increases by 1$ Y will increase by 11,85 points.
Coefficient a0 is the value of Dow-jones industrial average (Y) in case if a1 and a2 are both equal to 0.
t-Test
As through the whole investigation, these tests are supposed to be held due to Microsoft Excel functions («CTBro^PACnOEP», «F.OEP.nX»). In case of t-test it is necessary to apply for «CTtro^PACnOEP» function which let us define the t critical. It considers two parameters in order to calculate t critical:
T critical calculation Table 1
a= 0,05 t crit= 2,10
a= 0,01 t crit= 2,88
a= 0,1 t crit= 1,73
The sense of t-test states that if the absolute value of t statistics of each parameter is more than tcrit obtained above:
| t | >tcrit (1)
then we may conclude that parameter is significant for the model.
In case of this model, it is obvious that all coefficients a0, a1 and a2 are significant under the circumstance that a=0,05 within this model.
R2-Test
Concerning this test everything is rather simple and not go beyond the analysis of R2. According to this test if R2 is close to 1 means that specification is constructed in very good way because this parameter shows x variables influences
the y variable by linear regression. In this case R2=0,76 and it means specification is quite good: 76% of variances X1 and X2 describe variance Y by linear regression model within this model.
F-Test
This test also requires to calculate the Fcrit and to compare it with F given in regression analysis.
The function we are going to apply for has already been mentioned -«F.OEP.nX».
Table 2
F critical calcula tion
a= 0,05 F crit= 3,55
a= 0,01 F crit= 6,01
a= 0,1 F crit= 2,62
This tests checks the whole specification whether its quality is high or low and if R2 is random variable or not. If Fcrit is more than F of a model:
^rit^
then the quality is low and R2 is random. Otherwise, vice versa.
In this case according to the table above under a = 0,05 Fcrit <F, so we conclude that the quality of specification is high and R2 is not random within this model.
So the form of specification will be:
Yt = 8670,58 + 14,34X1t + 11,85X2t + et
(1148,42) (6,23) (1,67) (44,01) tstat [7,63] [2,30] [7,11] R2 = 0,758 F = 28,12 tcrit = 2,10; a = 0,05 ^c-rit = 3,55; a = 0,05 Goldfield - Quandt Test
According to Goldfield - Quandt test, we assume that = const. As a result of this test, we find out, if the residuals are homoscedastic or not and if we may use ordinary square to estimate parameters.
GQ coefficient calculation
Table 3
GQ= 1,17
1/GQ= 0,85
Fcrit= 3,44
Basing on these two inequalities, we compare our figures: GQ<Fcrit and 1/GQ<Fcrit so we can conclude the residuals are homoscedastic and we may use ordinary square to estimate parameters or coefficients of the model.
Durbin-Watson test The next step is to carry out Durbin-Watson test to check if there exists correlation between residuals. To calculate DW constant there is the formula
£(et - et-1)2 DW = ' * 1
Se2
DW=1,56
Defining the intervals means to find du and di in the table. In this model there are two regressors and sample size 21. Using table of values for Durbin-Watson criteria we find values di= 1,125 and du=1,538. Then make a table. Intervals:
Picture 1
Positive correlation no correlation Negative correlation
0 dl du 2 4-du 4-dl 4
0 1,125 1,538 2 2,462 2,875 4
dw_156
It is obvious that value of DW got into interval from du to 4-dl, that means that within this model there is no correlation between residuals. The third precondition of Durbin-Watson theory is valid so residuals are homoscedastic and coefficients are said to be exact.
Confidence interval and adequacy of the model Finally, it is important to estimate the adequacy of the model. For that, it is necessary to construct confidence interval. Interval is calculated:
jY - tcrit * a; Y + W * a) To estimate DJIA (Y) for 01.10.2014 we use coefficients a0, a1 and a2 and values X1 and X2.
Y = a0 + a1 * X1 + a2 * X2 = 16915,19
Baring in mind when calculating tcrit, level of significance taken is equal to
0,01.
Confidence Interval (16788,5;17041,87) Now DJIA01.10.2014 = 16804,71 is covered by confidence interval. Forecasts obtained are said to be correct with the probability of p=100 - a=99 (a=1%) and model is adequate.
Conclusion: despite the fact that these two companies are not considered in DJIA, the model constructed proves that they should be included in the list and reflect the trend of the whole market.
List of references
1.Трегуб А.В., Трегуб И.В. Методика прогнозирования показателей стохастических экономических систем — Вестник Московского государственного университета леса — Лесной вестник. 2008. № 2. С. 144— 151.
2.Трегуб А.В., Трегуб И.В. Методика прогнозирования основных показателей развития отраслей российской экономики — Вестник Московского государственного университета леса - Лесной вестник. 2014. № 4 (103). С. 231—236.
3.Шарп У.Ф., Александер Г.Дж., Бэйли Дж.В. Инвестиции — М.: Инфра — М, 2001.
4.Finam.ru.
Baryshnikov P. Y.
Bachelor of Economics, master student of International Finance Faculty Financial University under the Government of the Russian Federation
Russia, Moscow
USAGE OF THE ORDINARY LEAST SQUARES METHOD FOR PARAMETER ESTIMATION OF ECONOMIC GROWTH BY EFFECTS OF MACROECONOMIC VARIABLES IN BRICS COUNTRIES ON THE BASIS OF CAPITAL MARKET MODEL
Abstract. This article considers the results of the investigation of basic macroeconomic indicators of the BRICS countries using ordinary least squares method on the basis of capital market model and proves the applicability of this model to these countries.
Keywords: ECONOMETRICS, CAPITAL MARKET MODEL, BRICS, BRAZIL, RUSSIA, INDIA, CHINA, SOUTH AFRICA, GDP, INTERST RATE, INVESTMENTS, GROSS CAPITAL FORMATION.
Today, in the era of globalization and internationalization many scientists face the problem of global data research and economic modeling. Amounts of international trade as well as global output become significantly bigger. Especially, it concerns developing and newly industrialized countries such as BRICS. These countries show rapid economic growth year after year and there is an issue which models should be used for their economic analysis.
The aim of the current research is to investigate BRICS countries using part of capital market model and to find out whether this model is applicable to investigated countries or not.
This research is particular important because it helps to test the significance of factors that can potentially influence the capital markets of BRICS countries, as well as to conduct a study of the dependence between the main economic indexes. This research will allow us to draw some conclusions about whether the theory of capital markets is confirmed for the BRICS data or not.
However, first of all let's say some words about the capital market model in general and about countries which have been examined in the current research.
Capital market model consists of two equations and describes dependence of the real interest rate (Rt) on money supply (Mt) and real GDP (Yt). As well as dependence of the real GDP (Yt) on real interest rate (Rt) and gross capital formation (It) (Figure 1).
