Эконометрический анализ факторов в регрессионной модели для прогнозирования рыночной стоимости акции

ФРС.

Nowadays not so many companies can effectively manage their cash flows. Annually appears new methods of company’s management, all of them aimed on increase effectivity to satisfy growing consumers demand. Organization has three type of activities: operational, financial, investing activity. International companies diversify their activity – investing in shares, bonds and other financial instruments. Nevertheless not so many companies can effectively diversify cash flow to increase their funds. Stock exchange is not stable market and most amount of traders, companies face difficulties, to increase value of portfolio investment. Specialists use different instruments for trade and forecast share price, one of methods which can be applied – statistical. Analyzing historical values and factors, which influence on stock price, can be found events, which positively or negatively influence on price. Firstly, it may be annual reports about multinational company’s activity. Secondly, key rate of central bank influence on companies (shortage or increase of money supply). A lot of factors may influence on stock price, but statistical approach helps to specialist identify most significant of them and determine positive or negative impact on share price.

SnP 500 is index, which describes American economy, from the one side it’s difficult to describe it with only 5 variables. On another if it’s macroeconomic factors, it may influence on productivity of companies. Using econometric model analyzed macroeconomic data and commodity prices (For research were taken quarterly data from July of 2007 to July of 2016).

Table 1 – indicators definition

Y	SnP500 index
X1	global price of brent crude, u.s. dollars per barrel

X2	real gross domestic product, percent change from preceding period, quarterly, USA
X3	national currency unit per troy ounce gold price in us dollar, end of period
X4	foreign direct investment in u.s.
X5	effective federal funds rate, percent, not seasonally adjusted

One stage least square is one of the common methods of regression analysis for estimation unknown parameters. In model involves previous (historical) prices, in which should be minimized the sum of deviations [1]. This kind of analysis popular among investment funds for predicting shares, commodity prices on the market.

In addition other variables may influence on SnP 500 index and this model can be modified to identify better coefficients for forecasting stock price. In our econometric model mistake of approximation may reflect other factors, not only commodity prices, operational activity or macroeconomic indicators. Investor’s or political performance can change trend on stock price. Crisis 2008 year leave a strong imprint on institutional investors, mutual and pension funds. Pprejudices of many investors about the coming crisis may prompt withdraw investments from securities.

Table 1 – regression analysis

System: M

Estimation Method: Least Squares

Date: 02/10/17 Time: 10:32

Sample: 1 37

Included observations: 37

Total system (balanced) observations 37

	Coefficient	Std. Error	t-Statistic	Prob.
C(1)	-1017.825	178.6778	-5.696429	0.0000
C(2)	2.040564	0.868108	2.350589	0.0253
C(3)	20.56217	7.455613	2.757945	0.0097
C(4)	-0.274223	0.105522	-2.598714	0.0142
C(5)	0.000900	4.89E-05	18.41613	0.0000
C(6)	71.15476	18.26835	3.894975	0.0005

Determinant residual covariance        9690.026

Equation: Y=C(1)+C(2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5

Observations: 37

R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat

0.938374  Mean dependent var      1508.641 0.928434  S.D. dependent var       402.0037 107.5431  Sum squared resid       358530.9 1.191417

Based on regression analysis have been identified, that R – squared 93.83% (demonstrates high tightness of the link between Y and X). Probability of variables (Prob.) less than 5% which means high level of significance, moreover it confirms t - statistic. Durbin – Watson test equals = 1.19, it means that our model in the area of uncertainty, it means that some of the variables may reflects on our final results (correlation).

To accept model should be analyzed test on heteroscedasticity, it means that variance of the random error should constant or focused. If errors distributed without similarity it means that we can’t accept model. Heteroscedasticity is random distribution of errors, in which we can’t predict share price. Provided two type of tests on heteroscedasticity.

Table 2 – Glejser test

X1 = 31.75%	Prevails heteroscedasticity.
X2 = 81.3%	Prevails homoscedasticity.
X3 = 43.04%	Prevails heteroscedasticity.
X4 = 22.17%	Prevails heteroscedasticity.

X5 = 61.66%

Prevails homoscedasticity.

Breusch – Pagan – Godfrey test demonstrates that variables from equation equals 38.64% (it means that with 61.36% we can accept appearance of heteroscedasticity). Nevertheless we have two variables, which demonstrates focused distribution of errors – x2(real GDP), x5(effective federal fund rate).

			Table 3 –	correlation
	y	x1	x2	x3	x4          x5
y	1
x1	0,220106478	1
x2	0,40737528	0,158247195	1
x3	0,129127296	0,413278319	0,338141942	1
x4	0,909713811	0,298352752	0,328064357	0,31987138	1
x5	0,116124171	0,0393729	0,165729026	0,575617426	0,410052529  1

Equation of SnP 500:

SnP500 = -1017.82 + x1 * 2.04 +x2 * 20.56 + x3 * (-0.274)+x4 * 0.0009+x5 * 71.15

Let’s give explanation of calculated equation. It means that SnP500 will change if one of the “x” factors vary, some of them has positive impact, the others negative. The most significant factors are: real GDP; effective federal fund rate.

Thus, analysis of factors affecting on the SNP 500 index demonstrated that only two of the five factors have passed all the tests, unlike the other three, in which were found correlation and heteroscedasticity. Growth of GDP and effective federal funds should increase stock price of SnP500. This model can be used to forecast, but for a more accurate analysis, it can be used in a more extensive analysis, which will more accurately reflect the influences and to predict the price.