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International Journal of Economics and Finance; Vol. 10, No. 5; 2018
ISSN 1916-971X E-ISSN 1916-9728
Published by Canadian Center of Science and Education
197
Investigation of Co-Integration between Standard and Poor Index and
Dow Jones Index in the New York Financial Market
Ateyah Alawneh1
1 College of Business, Tafila Technical University, Jordan
Correspondence: Ateyah Alawneh, College of Business, Tafila Technical University, Jordan. E-mail:
ateayh1@yahoo.com
Received: March 7, 2018 Accepted: March 28, 2018 Online Published: April 15, 2018
doi:10.5539/ijef.v10n5p197 URL: https://doi.org/10.5539/ijef.v10n5p197
Abstract
The study investigates the co-integration between (the S&P 500 index)and (Dow Jones index) the DJIA by
busing the method Engle-granger co-integration Test. The study use annual data from 1990 to 2016.The study
examines the stability of the index of S&P 500 and DJIA using the E-views program through a unit root test. The
study found that the indicators are unstable, but they become stable when taking the first difference. This
condition integrates (the S&P 500 index) and (the DJIA index) during the long-term co-integration test. The
analysis shows that there is a negative co-integration between the two variables. It should be emphasized that the
short-term dynamic analysis showed a positive co-integration between both indexes. The study concluded that
there is an urgent need to take into account the long-term negative co-integration between (the S&P 500 index)
and (the DJIA index) by investors in the New York market. Also, the study considers short-term positive
integration between (the S&P 500 index) and (DJIA index), which turns into a negative relationship in the long
term when taking into account the markets linked with the New York market as a major global market and
other international financial markets when making any financial investment. The result of this study could help
users of major international financial markets in investment diversification to reduce risk.
Keywords: financial indexes, financial market, major global financial markets, major global indicators,
diversification of portfolio
1. Introduction
The main financial indicators plays a major role in influencing the financial markets if they increase or decrease
indicators on the state of financial market and indicators that contain a large industrial, service companies and
contacts. In the case of market activity, the rise and stagnation that occurs in the case of financial market decline
is reflected via investment decisions. The current study investigates the co-integration of financial indicators in a
major global financial market, namely the New York Financial Market (NYFM), which is one of the world major
financial markets like the London and Tokyo Market. The S&P 500 index and Dow Jones (DJIA) index were
also selected because they represent major indexes on the NYFM and have weight in the US Financial Market .
The index of S&P 500 was chosen because it consists of five hundred securities representing 80% of the market
value of shares traded on the New York Stock Exchange (NYSE). The Dow Jones index was chosen because it
contains 30 securities, representing 30% of the NYSE.
(http://www.arab-api.org/images/training/programs/1/2004/44_C9-4.pdf)
The study investigates the co-integration of these indexes by using the Engel-Granger test method, which is used
in the case of co -integration between the two variables only. Therefore, the study will investigate whether or not
there is a co-integration between the S&P 500 index and the Dow Jones index. Also the study aims to identify it
is long-term or short-term co- integration in the US Financial Market. This is considered important for investors
and traders in the global financial markets, especially when investors diversify in the financial market.
Several studies have been conducted on co-integration that consider some variables. Vikkram Singh, Eduardo
Roca and Bin Li’s study (2017) reveals that there is co-integration between global finance markets, and that the
major global financial markets offered to the impact and interdependence with each other more than other market.
Study by Bhuvaneshwari and Ramya’s (2017) aims to determining the co-integration and the causal relationship
between stock prices and the exchange rate. by using the unit root test the study found that the data were
stabilized at the first difference, however it found that no integration between the study’s variables. Conversely,
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Vishal and Peo’s study (2014) showed the co-integration of some economic variables in the Indian stock market.
The study considered four indicators in the financial market, including: SMALL CAP, CNX NIFTY, CNX
NIFTY 500 and CNX MID CAP. The study used the Engel-Granger test and Johansson co-integration testing.
The analysis showed that there is co-integration between the four variables.
Ferreira and Oliveira’s study (2014) found an integration between the Portuguese financial market and the
emerging European Markets (Italy and Ireland). They also found that the quality of integration between the
European markets and mature markets (France, the UK, Germany and the United States). In addition, the Balq
Abdullah and Bashir (2013) examines the existence of a long-term relationship between savings and investment
in the Libyan economy; the data was taken from 1970-2005 and the study used the Engel-Granger test and
Johansson co-integration testing. The analysis shows that there is no co-integration between savings and
investment during the study period. This is due to the nature of the economy of the Libya which is dependent on
oil as its main source. A study conducted by, Sazali, Chase, Kwan-Lyn, and Azilawati (2013) took a sample from
the following countries: New Zealand and Hong Kong, Australia, Japan, South Korea, Thailand. The study used
a unit root test and Engel-Granger test, and the results of the study showed that there is no long-term correlation
between Indonesian stock markets and exchange rates in the study sample.
Another study was conducted based on the analysis of the co-integration of indicators in three financial markets
(Assidenou, 2011). Results indicated that there was a co-integration between capital markets in Asian countries
where investors couldn’t avoid any external impact from these financial markets. Hande Erdinc and Joniada
Milla’s study (2009) assessed the fact that whether or not there is co-integration between the financial markets of
the (EU) countries, France, Germany and the UK, where the study used unit root tests and co-integration tests.
Through monthly data on securities for the period from January 1991 to September 2000, the study found that
there is long-term co-integration between the EU countries in the study sample. Taimur (2011) by using
co-integration test found that there is no co-integration of financial markets in China, Korea, Malaysia and
France with the United States Financial Market where investors can make gains from investment diversification
with America. Hwey-Yun and Chien-Chung (2009) identified the co-integration of stock prices and the exchange
rate in Japan and Taiwan, where the results of the tests show no short-term relationship between the two
countries. However, in the long run there is a positive relationship.
A review of previous studies showed the integration of relationships between financial market indicators with
some countries (Taimur, 2011; Vikkram, Eduardo, & Bin, 2017; Hande & Joniad, 2009). There are also applied
studies that focused on the variables in financial markets and monetary markets, but dealt with partial issues (e.g.
Sazali, Chase, Kwan-Lyn, & Azilawati, 2013). However, the present study is distinguished from its predecessors
as the first study within the scope and science of the researcher that integrates the S&P 500 and DJIA indices
using financial data for these indicators during the study period. It is also the first study within the scope and
science of the researcher to use the Engel-Granger test and the E-views software program to test co- long-term
and short-term integration between the study indices in the New York financial market as one of the world’s
major financial markets.
The next section introduces the general framework of the study. Second two covers the theoretical framework of
the study; the third section is the econometric analysis. While the fourth section contains results of the study. The
fifth section presents the study recommendations ,and the last section references.
1.1 The Study Problem
The study problem comes from the statement of the complementary relationship between the S&P 500 index and
the DJIA index of the NYFM a way to understand the financial behavior of financial indicators in the NYFM,
which is one of the major financial markets in the world. Because of it’s size, it affects the behavior of investors
in the market and the behavior of investors in other financial markets that are linked to the NYFM, which can
lead to understanding the activity of the financial market. This affects general investment decisions and
consequently the general economic situation which is reinforced accordingly. The problem of the study is
formulated through the following questions: 1. Is there a positive co-integration that is statistically significant in
the long-term between the S&P500 index and the DJIA index? 2. Is there a positive co-integration that is
statistically significant in the short- term between the S&P 500 index and the DJIA index?
1.2 The Study Hypotheses
The hypotheses of the study are formulated as following,
1). There is a positive co-integration that is statistically significant in the long- term between the S&P 500 index
and the DJIA index.
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2). There is a positive co-integration that is statistically significant in the short- term between the S&P 500 index
and the DJIA index.
1.3 The Importance of the Study
The importance of the study is highlighted by its presentation of the ways and the methods of co-integration
using the Engel-Ganger test. It is important that investors should know the financial behavior of the main
indicators in the long term and in the short term, which contributes to strengthening the theoretical aspect of the
main financial markets, and contributes to strengthening the practical side of the field of financial markets,
especially the main indicators in the global financial markets. This is a study of investors in the NYFM, which
can help in understanding the behavior of investors in other financial markets interconnected with the former
market.
It also helps investors diversify the financial portfolio in the NYFM and in international diversification. It also
helps to understand the behavior of investment decisions and the general economic situation.
1.4 Objectives of the Study
This study aims to:
1). Enhance the theoretical and practical aspects of financial markets and major global indices in major financial
markets through the use of the Engel-Ganger test.
2). Clarify the stability of the index of S&P 500 and the DJIA index and degree of stability.
3). Test relationship dynamic integration in the short-term between the S&P 500 index and the DJIA index.
4). Test long-term co-integration between the S&P 500 index and the DJIA index.
5). Make recommendations that help investment decision makers understand the behavior of the dynamic
relationship of key financial indicators in the long- term and short term.
1.5 The Procedural Definitions
1- Dow Jones (DJIA)
This index contains 30 securities representing 30% of the New York Stock Exchange. (arab-api).
2- Standard & Poor (S&P500)
This index consists of 500 securities, representing 80% of the market value of shares traded on the New York
Stock Exchange. (400 industrial companies, 40 public benefit companies, 20 transport companies and 40
companies in finance, banking and insurance) (arab-api).
1.6 The Boundaries of the Study
Spatial: The study will be applied to the main financial indicators in the New York financial market.
Temporal: The study will cover the period of (1990-2016) to provide a historical series of statistical financial
data for the variables of the study.
1.7 The Society and the Sample of the Study
The study population consists of the S&P 500 index and the DJIA index.
2. Methodology of the Study
The standard analytical approach will be based on the use of the Engel-Ganger test method to deal with the study
data to reach the objective of the study Through the following.
2.1 Data Sources
The study will be based on the financial statements issued by the New York financial market during the period
(1990-2016).
2.2 Statistical Tests Used in the Study
2.2.1 Unit Root Test
The purpose of conducting this test is to test the indicators of the study; this test is necessary before applying
tests.
2.2.2 Engle-Granger Co-Integration Test
A. Test the co-integration in the long-term between the S&P 500 and DJIA indices.
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A.1- Co-integration in the long- term goes through two steps
Step (1): Estimate the linear relationship in the normal lower squares method.
Step (2): Obtain the residuals (Et = values -estimated values) obtained from the first step.
If the residual method is static at the level indicated by the existence of a co-integration between the variables,
then the relationship estimated in the first step is correct yet not a misleading relationship. If the residual method
is not static at the level, then it does not indicate a long-term equilibrium relationship between the variables and
cannot be relied upon (Balq & Bashir, 2013).
B.Test the co-integration in the short-term between the S&P 500 and DJIA indices.
The short term relationship will be estimated through the following steps.
Step (1): Take the first difference of the dependent and independent variables.
Step (2): Add the extracted residue in the long-term model as an independent variable to the current model in the
first step with a lag (-1).
3. Theoretical Framework: Definition of Financial Indicators and Their Importance and the Relationship
between the S&P 500 Index and the DJIA index
3.1 Definition of Financial Indicators in Financial Markets and Their Importance
3.1.1 Definition of Financial Indicator
The stock market index measures the level of prices in the market. It is based on the sample of the shares of
establishments traded in organized and unorganized capital markets. The sample is often selected in such a way
that the index can reflect the situation in which the capital market measure (http://www.arab-api.org).
When the expected movement of the index goes up, it is called the (market bull) and when the expected
movement of the index is going down it is called the (market Bear).
3.1.2 The Standard & Poor (S&P 500) Index
The S&P 500 contains five hundred securities, representing (80%) of the market capitalization of the New York
Stock Exchange (400 industrial companies, 40 public benefit companies, 20 transport companies, 40 companies
in the field of finance Banks and insurance). The S&P includes common shares listed on the New York and
(NASDAQ) Stock Exchanges. It was first calculated in 1923 and is currently one of the best general indices of
the US stock market and it is calculated by S&P and Dow Jones. Standard & Poor 500 is a weighted index of
market value, with companies weighted according to the total market value of their issued shares. The higher the
market weights of the company, the greater the impact on the index (https://www.argaam.com).
3.1.3 The Dow Jones Industrial
This index contains 30 securities, representing 30% of the New York Stock Exchange and is the oldest indicator
of the US stock market. It dates back to 1896 and tracks the movement of 30 large US companies, but currently
it does not rely on industrial companies despite its name. It additionally includes companies from various
categories, such as finance and consumer goods, including: Goldman Sachs, Visa and McDonald’s. This index
was developed by Charles Dow and was first calculated on May 26, 1896, and is now managed by S&P Dow
Jones. The Dow Jones Industrial Average is a weighted average for the price. The companies listed on the index
are weighted in proportion to their share price, so the higher stocks have higher weight and therefore have a
greater impact on the performance of the index. It was originally calculated by the total share price of each listed
company and divided by the number of companies, so it is called the average, but the index is no longer
calculated in that simple way, because over the years the divestitures and other events have made the Dow a very
small number (number less than 0.2)(https://www.argaam.com).
3.2 The Importance of Financial Indicators in the Stock Market
Recently, there have been many usages and uses of financial indicators in the stock market to individual
investors and other parties that deal with such “capital” markets, the most important are the following.
1). Giving a quick idea of the performance of the portfolio, where the investor or the investment manager can
make a comparison between the change in the yield of his portfolio (positive or negative) with the change in the
market index as reflecting a portfolio of good diversification without the need to follow the performance each
sheet separately. If investment (for an investor) in a particular industry has its own index, then it would be better
to follow that indicator.
2). Judging the performance of professional managers, according to the notion of diversification, an investor who
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has a portfolio of randomly-selected-securities can achieve a return that is almost equivalent to the market return
(average rate of return on securities traded in the market) reflected in the index. This means that a professional
manager who uses advanced diversification techniques is expected to achieve higher returns than average market
returns.
3). Predicting the state of the market: If the analyst knows the nature of the relationship between some economic
variables and the variables of the financial indicators (the so-called basic analysis), he or she may be able to
predict in advance what the case of the market in the future will be. Technical and historical indicators that
measure the state of the market may reveal a pattern of changes that occur. If the analyst knows this pattern, he
or she can’t predict future developments in the direction of price movement in the market.
4). Investors use the portfolio risk assessment to measure the systemic risk of the portfolio, the relationship
between the rate of return of the risky assets and the rate of return of the market portfolio of the risk assets
(www.arab-api.org)
3.3 The Relationship between the Indicator (S&P 500) and the (DJIA) Index
Table (1) shows that the S&P 500 index was at 330.22 points in 1990, as it continued to rise and fall during the
years of the study until it reached 2,238.83 points in 2016. The study note the continued rise of the DJIA index,
finding that it was at 2,633.66 points in 1990, and that it reached 1,762.6 points in 2016.
Table 1. Size of the S&P 500 index and the DJIA index during the years of study (1990-2016)
years
S&P 500
DJIA
1990
330.22
2633.66
1991
417.09
3168.83
1992
435.71
3301.11
1993
466.45
3754.09
1994
459.27
3834.44
1995
615.93
5117.12
1996
740.74
6448.27
1997
970.43
7908.3
1998
1229.23
9181.43
1999
1469.25
11497.12
2000
1320.28
10787.99
2001
1148.08
10021.57
2002
879.82
8341.63
2003
1111.92
8341.63
2004
1211.92
10783.01
2005
1248.29
10717.5
2006
1418.3
12463.15
2007
1468.36
13264.82
2008
903.25
8776.39
2009
1115.1
10428.05
2010
1257.64
11577.51
2011
1257.6
12217.56
2012
1426.19
13104.14
2013
1848.36
16576.66
2014
2058.9
17098.45
2015
2043.94
17425.03
2016
2238.83
19762.6
Source: https://sa.investing.com/indices/us-30-historical-data.
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Years (1990-2016)
Figure 1. The graph of the index S&P 500 during the years of study
Source: By the researcher based on the data of Table 1.
From the graph above, we see the continued growth of the index of S&P 500 during the years of study. We also
notice the rise and growth of the index until it reached the summit level in (2000) and then dropped in (2002),
then rose and continued to rise until the peak reached in (2007) and the study note the continued rise and fall of
the index during the years of study.
Years (1990-2016)
Figure 2. The DJIA chart for the years of study
Source: By the researcher based on the data of Table 1.
From the graph above, the study see the continued growth of the DJIA index during the years of study. We also
notice the rise and growth of the index until the peak was reached in (2000) then decreased in 2002 and then rose
and continued to rise until reaching the peak in 2007. We further notice the continued rise and fall of indicators
during the years of the study; it would decrease at a certain point and then rise in height and so on. The rise and
fall of the indices is due to the impact of stock indices in general on a number of factors including: corporate data
and economic reports, domestic and foreign political events, wars and terrorism and natural disasters that may
0
4,000
8,000
12,000
16,000
20,000
90 92 94 96 98 00 02 04 06 08 10 12 14 16
DJIA
0
400
800
1,200
1,600
2,000
2,400
90
92
94
96
98
00
02
04
06
08
10
12
14
16
S
&
P
5
0
0
index S&P
500
DJIA
index
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have economic effects.
The correlation between the S&P 500 index and the DJIA index is noted below as thus:
1). The S&P 500 index and the DJIA index reached the summit during the same years (2000) and (2007).
2). The S&P 500 index and the DJIA index access to the lowest point during the same school years in 2002 and
2008.
3). It is noted that the relationship exists between the indicators of rise and fall during the same years.
4. The Practical Framework of the Study: Econometric Analysis
4.1 Test the Stability of the S&P 500 Index and the DJIA Index
4.1.1 Test the Stability of the S&P 500 Index
Note from Table 1 that the Dickey-Fuller test statistic is equal to (-0.468448), while the critical value is at 5%
equal to (-2.981038). This indicates that the series is not static as shown in Appendix 1, but the series is static by
taking the first difference using the Dickey-Fuller test statistic as shown in Appendix 2. This can be summarized
in Table 2 below.
Table 2. Summary of the stability test of the index of S&P 500
Augmented Dickey-Fuller test statistic
Test critical values(5% level)
Result
-0.468448
Prob.*(0.8823)
-2.981038
D-F (Augmented Dickey-Fuller test statistic) <T.V
(Test critical values(5% level ) No Stationary
-4.300456
Prob.*(0.0000)
When making the first difference
-2.986225
D-F>T.V Stationary
Note from Table 2 that the index of S&P 500 is stable after the first difference.
4.1.2 Test the Stability of the DJIA Index
Note from Table 3 that the Dickey-Fuller test statistic is equal to (-0.211557), which is greater than the critical
value at 5%, which equals(-2.981038). This indicates that the series is not static, as shown in Appendix 3, and
the series is static by taking the first difference using the Dickey-Fuller test statistic, as shown in Appendix 4.
This can be summarized in Table 3.
Table 3. Summary of the stability test of the index of DJIA
Augmented Dickey-Fuller test statistic
Test critical values(5% level)
Result
-0.211557
Prob.*(0.9252)
-2.981038
D-F<T.V No Stationary
-4.825170
Prob.*(0.0007)
-2.986225
D-F<T.V Stationary
It can be noticed that, from Table 2 and Table 3, the series of S&P 500 and the DJIA series have been stabilized
after the first difference, meaning that the indicators are stabilized at the same score. This is the achievement of
the first condition for the co-integration of indicators using the method of Engel-Granger test.
4.2 The Co-Integration of the Long-Term between the S&P 500 Index and the DJIA Index
In order to estimate the model co-integration between the S&P 500 index and the DJIA index we will estimate
the following model, using the residual method to correct the error to estimate the model in the long term as
follows. DJIA = a +B s&p500 + Et
Whereas:
DJIA: values the DJIA index during the years of study;
A: constant in the equation;
B: Regression parameter to be estimated;
S&P 500: values of the index during the years of study;
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Et= DJIA - DJIA(estimated);
Where residual methods are intended to correct error and estimate the model in the long term.
The S&P 500 is the best representation of the US market, as it contains 500 companies from large companies in
the sense that it contains 500 securities representing 80% of the market value of traded shares on the New York
Stock Exchange (400 industrial companies, 40 public utility companies, 20 transport companies, 40 companies
in the finance, banking and insurance sectors), compared with the Dow Jones index, which contains 30 securities
representing 30% of the New York Stock Exchange
The model will be estimated using the E-views program as follows. It can be noted that, from Appendix (5),
the normal model is estimated where
results are shown but these results are not for the long term.
DJIA = -167.5541 + 8.782450 S&P500
(***32)0.49) ) t:
In order to estimate the integration, the model will be estimated using the following equation.
ET= DJIA – DJIA (estimated)
The residual values are calculated using the (E-views) program, as shown in Appendix 6. Then the integration of
the subscriber are performed by using the unit root using a program (E-views) where the co-integration model
was estimated in the long run and the results were shown in Appendix 7, where the value of Dickey-Fuller is not
statistically significant and the constant value of the model is not statistically significant. In order to obtain the
stability of the model, the first difference will use the (E-views) program. It is also noted in Appendix 8 that the
model is stable, thus indicating the statistical significance of Dickey-Fuller. But the study noted that the constant
is not a statistical significance, and it must be deleted, as is noted in Appendix 9 after the deletion of the constant,
which gets the following form:
DJIA = -1.318167D(ET-1)
Table 4. Results of regression model
Dependent Variable: DJIA
Variable
Coefficient
t- Statistic
Prob.
D(ET(-1))
-1.318167
-6. 7
0.0000
R- Squared: 65%
Adjusted R- Squared: 65%
Durbin-Watson stat: 2.03
The model shows that the adjusted R-Squared (65%), which also shows that the change in the independent
variable accounts for about (65%) of changes in the dependent variable. The Durbin-Watson stat is equal to
(2.03), meaning that the model is suitable and statistically significant, where there is no problem of
auto-correlation or systematic error
Note that the combined integration between the S&P 500 index and the DJIA index is negative, whereas the S&P
500 index increases lead to reduced DJIA in the long term. It rejects the hypothesis in which there is a positive
co-integration that is statistically significant in the long term between the S&P 500 index and the DJIA index.
4.3 The Co-Integration of the Short-Term between the S&P 500 Index and the DJIA Index
In order to estimate the co-integration model between S&P500 and DJIA, the study will use the residual method
to correct the error to estimate the model in the short term by estimating the following model.
D(DJIA) = a +B1 D(P&S500) +B2 et(-1)
+
ut
Whereas :
D (DJIA): The first difference (D) DJIA;
a: constant in the equation;
B, B2: Regression parameters to be estimated;
P & S: The first difference of S&P 500.
Et(-1): DJIA-DJIA(estimated) where the residual methods are intended to correct the error and estimate the
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model in the short term. These are the same values that were estimated using equation number (2) but the values
are lag (-1).
The model of co- integration was estimated in the short term and the results as shown in Appendix (10) where it
appears that the model is statistically significant, but the constant is not statistically significant. Therefore, the
estimate will be regained in the short term with the deletion of the constant as in Appendix (11).
Where the results are as follows:
D( DJIA) = 7.462409 D(P&S500) - 0.472095 ET(-1)
T: (13.63555)**** (-2.907086)***
Table 5. Results of regression model
Dependent Variable: D(DJIA)
Prob.
Coefficient
t- Statistic
Prob.
D(P&S500)
7.462409
13.63555
0.0000
ET(-1)
-0.472095
-2.907086
0.0077
R- Squared: 86%
Adjusted R- Squared: 85%
Durbin-Watson stat: 2.22
It is clear from the model that adjusted R-Squared (85%) shows that the change in the independent variable
accounts for about 85% of changes in the dependent variable, and that the value of Durbin-Watson stat is the
model is suitable and statistically significant where there is no problem of auto-correlation or systematic error.
This equation is in for short term, where ET (-1) is added to the equation, which can be defined as a unit for the
regression of the combined integration and its value (-0.47) for the equilibrium at the present moment of (the
DJIA index.) If the value of zero is not necessary, the equilibrium gets to equilibrium point, while the
equilibrium value in the equation doesn’t get to zero, so there is a balance between the two indices. The value of
the error correction coefficient (equilibrium or residual index) is negative and statistically significant, and is
different from zero, and we note from the regression unit where the imbalance corrects the equilibrium at an
annual rate (-0.47). Also, the coefficient of S&P 500 equals (7.46) in the above model, which means an increase
of 1% in the index of S&P 500 on S&P 500 (-1) leading to an average positive increase of (7.46%) for (the DJIA
index) on DJIA (-1), it accepts the hypothesis in which there is a positive co-integration, which is statistically
significant in the short term between the S&P 500 index and DJIA index.
4.4 The Long-Term Model and Short-Term Model
Consequently, a long-term model and a short-term model could be incorporated as follows.
D(DJIA) = 7.462409 D(PS500) - 0.472095 ET(-1) - 1.318167D(ET-1)
long-term Short- term
The analysis shows that the long-term integration between the S&P 500 index and the DJIA index is inverse,
while the short-term co-integration between S&P 500 index and DJIA index is positive, Also the balance
between the two indices is equal (-0.47).
5. Results
We have come up the following results:
1). There is stability for the two indicators after the first difference and this is the first condition to achieve
co-integration in the sense that the two indicators are stabilized at one degree.
2). There is a long-term negative co-integration between the two indices, which means that an increase of the
S&P 500 index leads to a lower DJIA index value in the long term, and this result helps investors decide to
diversify their long-term investment portfolio.
3). There is a long-term negative co-integration between the two indices, which means that an increase of (the
S&P 500 index) leads to a lower (DJIA index) value in the long term, and this result helps investors decide to
diversify in investment portfolio. It rejects the hypothesis in which there is a positive co-integration statistically
significant in the long term between (the S&P 500 index) and the (DJIA index).
4). There is a positive dynamic short-term correlation between the index of S&P 500 and DJIA, which means a
one percent increase of (the index S&P 500)on S&P 500 (-1) leads to a positive increase of (7.46%) for DJIA on
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206
DJIA (-1). It accepts the hypothesis in which there is a positive co-integration which statistically significant in
the short term between (the S&P 500 index )and (DJIA index).
5). The study Recognized the balance between (the S&P 500index) and( DJIA index) at an annual rate (-0.47).
6. Recommendations
1). The long-term negative correlation between the S&P 500 index and the DJIA index should be taken into
account by investors in the New York market, especially when considering diversification of the portfolio.
2). There is an urgent need to consider the short-term positive co-integration relationship between (the S&P 500
index) and (the DJIA index), which turns into a long-term negative relationship by dealers.
3). There is a necessity to consider the relationship of long- and short-term integration between the two
indicators when diversifying investment portfolios or making any financial investment in the market New York
or other global markets linked to the New York financial market.
4). There must be a forecasting of the changes between the S&P 500 index and (the DJIA index) as well as their
impact on the markets linked to the New York market as a major global market and other international financial
markets.
5) Conduct future studies on the co- integration of other indicators in the New York financial market. Conducting
studies on the co-integration of key indicators in the New York financial market and indices in markets around
the world. Also conducting studies in the co- integration between New York financial market and other countries.
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Notes
Note 1. The short-term sequence of the short-term pattern must have a negative value and a statistical function
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207
until the dynamic model is stabilized in the short term.
Note 2. The Dickey-Fuller values are compared with McKinnon tables in a single independent variable (-3.34),
since the Dickey-Fuller value should be less than (-3.34) statistic (McKinnon) to be statistically significant.
Dickey-Fuller is equal to (-6.7), which is less than the statistic (McKinnon). as shown in appendix (12).
Appendix 1
Null Hypothesis: S&P500 has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-0.468448
0.8823
Test critical values:
1% level
-3.711457
5% level
-2.981038
10% level
-2.629906
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(S&P500)
Method: Least Squares
Date: 11/16/17 Time: 16:40
Sample (adjusted): 1991 2016
Included observations: 26 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
S&P500(-1)
-0.039204
0.083690
-0.468448
0.6437
C
116.9132
100.9054
1.158642
0.2580
0.009061
R-squared
73.40808
Mean dependent var
-0.032229
Adjusted R-squared
198.0291
S.D. dependent var
201.1949
S.E. of regression
13.52023
Akaike info criterion
971505.1
Sum squared resid
13.61701
Schwarz criterion
-173.7630
Log likelihood
13.54810
Hannan-Quinn criter.
0.219443
F-statistic
1.734772
Durbin-Watson stat
0.643691
Prob(F-statistic)
Appendix 2.
Null Hypothesis: D(S&P500) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-4.300456
0.0026
Test critical values:
1% level
-3.724070
5% level
-2.986225
10% level
-2.632604
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(SP500,2)
Method: Least Squares
Date: 11/16/17 Time: 16:42
Sample (adjusted): 1992 2016
Included observations: 25 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(S&P500(-1))
-0.899190
0.209092
-4.300456
0.0003
C
65.95922
43.50946
1.515974
0.1432
R-squared
0.445702
Mean dependent var
4.320800
Adjusted R-squared
0.421602
S.D. dependent var
270.0824
S.E. of regression
205.4044
Akaike info criterion
13.56446
Sum squared resid
970392.3
Schwarz criterion
13.66197
Log likelihood
-167.5557
Hannan-Quinn criter.
13.59150
F-statistic
18.49392
Durbin-Watson stat
1.943958
Prob(F-statistic)
0.000266
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208
Appendix 3.
Null Hypothesis: DJIA has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-0.211557
0.9252
Test critical values:
1% level
-3.711457
5% level
-2.981038
10% level
-2.629906
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DJIA)
Method: Least Squares
Date: 11/16/17 Time: 16:37
Sample (adjusted): 1991 2016
Included observations: 26 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
DJO(-1)
-0.015517
0.073347
-0.211557
0.8342
C
807.2738
765.6874
1.054312
0.3022
R-squared
0.001861
Mean dependent var
658.8054
Adjusted R-squared
-0.039728
S.D. dependent var
1531.309
S.E. of regression
1561.430
Akaike info criterion
17.61840
Sum squared resid
58513530
Schwarz criterion
17.71517
Log likelihood
-227.0391
Hannan-Quinn criter.
17.64626
F-statistic
0.044757
Durbin-Watson stat
1.986143
Prob(F-statistic)
0.834239
Appendix 4.
Null Hypothesis: D(DJIA) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-4.825170
0.0007
Test critical values:
1% level
-3.724070
5% level
-2.986225
10% level
-2.632604
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(DJIA,2)
Method: Least Squares
Date: 11/16/17 Time: 16:38
Sample (adjusted): 1992 2016
Included observations: 25 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(DJO(-1))
-1.031623
0.213800
-4.825170
0.0001
C
682.4607
343.2625
1.988160
0.0588
R-squared
0.503049
Mean dependent var
72.09600
Adjusted R-squared
0.481443
S.D. dependent var
2215.670
S.E. of regression
1595.524
Akaike info criterion
17.66441
Sum squared resid
58551060
Schwarz criterion
17.76192
Log likelihood
-218.8051
Hannan-Quinn criter.
17.69146
F-statistic
23.28227
Durbin-Watson stat
1.958756
Prob(F-statistic)
0.000072
Appendix 5.
Dependent Variable: DJIA
Method: Least Squares
Date: 11/16/17 Time: 19:22
Sample: 1990 2016
Included observations: 27
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209
Variable
Coefficient
Std. Error
t-Statistic
Prob.
S&P500
8.782450
0.270283
32.49358
0.0000
C
-167.5541
340.3339
-0.492323
0.6268
R-squared
0.976870
Mean dependent var
9945.632
Adjusted R-squared
0.975944
S.D. dependent var
4612.986
S.E. of regression
715.4670
Akaike info criterion
16.05494
Sum squared resid
12797325
Schwarz criterion
16.15092
Log likelihood
-214.7416
Hannan-Quinn criter.
16.08348
F-statistic
1055.833
Durbin-Watson stat
1.039189
Prob(F-statistic)
0.000000
Appendix 6.
1990
-98.926427
1991
-326.68783
1992
-357.93704
1993
-174.92954
1994
-31.521556
1995
-124.70012
1996
110.31234
1997
-446.89853
1998
-1446.6665
1999
-1238.9401
2000
-639.74854
2001
106.16929
2002
782.20924
2003
-1256.1973
2004
306.93771
2005
-77.989989
2006
174.55574
2007
536.57631
2008
1011.1964
2009
802.29448
2010
699.90411
2011
1340.3054
2012
746.25222
2013
511.08544
2014
-816.18151
2015
-358.21606
2016
267.74232
Appendix 7.
Null Hypothesis: ET has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-2.894024
0.0597
Test critical values:
1% level
-3.711457
5% level
-2.981038
10% level
-2.629906
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ET)
Method: Least Squares
Date: 11/16/17 Time: 19:28
Sample (adjusted): 1991 2016
Included observations: 26 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
ET(-1)
-0.519906
0.179648
-2.894024
0.0080
C
8.748770
125.6827
0.069610
0.9451
R-squared
0.258696
Mean dependent var
14.10264
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210
Adjusted R-squared
0.227808
S.D. dependent var
729.2098
S.E. of regression
640.7891
Akaike info criterion
15.83708
Sum squared resid
9854656.
Schwarz criterion
15.93386
Log likelihood
-203.8821
Hannan-Quinn criter.
15.86495
F-statistic
8.375373
Durbin-Watson stat
2.046243
Prob(F-statistic)
0.007971
Appendix 8.
Null Hypothesis: D(ET) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-6.572767
0.0000
Test critical values:
1% level
-3.724070
5% level
-2.986225
10% level
-2.632604
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ET,2)
Method: Least Squares
Date: 11/16/17 Time: 19:30
Sample (adjusted): 1992 2016
Included observations: 25 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(ET(-1))
-1.317756
0.200487
-6.572767
0.0000
C
20.48157
144.0555
0.142178
0.8882
R-squared
0.652575
Mean dependent var
34.14879
Adjusted R-squared
0.637469
S.D. dependent var
1196.140
S.E. of regression
720.2023
Akaike info criterion
16.07356
Sum squared resid
11929901
Schwarz criterion
16.17107
Log likelihood
-198.9195
Hannan-Quinn criter.
16.10060
F-statistic
43.20127
Durbin-Watson stat
2.039182
Prob(F-statistic)
0.000001
Appendix 9.
Null Hypothesis: D(ET) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=6)
t-Statistic
Prob.*
Augmented Dickey-Fuller test statistic
-6.713979
0.0000
Test critical values:
1% level
-2.660720
5% level
-1.955020
10% level
-1.609070
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(ET,2)
Method: Least Squares
Date: 11/16/17 Time: 19:33
Sample (adjusted): 1992 2016
Included observations: 25 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(ET(-1))
-1.318167
0.196332
-6.713979
0.0000
R-squared
0.652269
Mean dependent var
34.14879
Adjusted R-squared
0.652269
S.D. dependent var
1196.140
S.E. of regression
705.3482
Akaike info criterion
15.99444
Sum squared resid
11940386
Schwarz criterion
16.04319
Log likelihood
-198.9305
Hannan-Quinn criter.
16.00796
Durbin-Watson stat
2.036683
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211
Appendix 10.
Dependent Variable: D(DJIA)
Method: Least Squares
Date: 11/16/17 Time: 19:43
Sample (adjusted): 1991 2016
Included observations: 26 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(S&P500)
7.250724
0.585946
12.37439
0.0000
ET(-1)
-0.461836
0.162654
-2.839382
0.0093
C
121.7878
120.7364
1.008708
0.3236
R-squared
0.870402
Mean dependent var
658.8054
Adjusted R-squared
0.859132
S.D. dependent var
1531.309
S.E. of regression
574.7358
Akaike info criterion
15.65386
Sum squared resid
7597387.
Schwarz criterion
15.79903
Log likelihood
-200.5002
Hannan-Quinn criter.
15.69567
F-statistic
77.23583
Durbin-Watson stat
2.343840
Prob(F-statistic)
0.000000
Appendix 11.
Dependent Variable: D(DJO)
Method: Least Squares
Date: 11/16/17 Time: 19:44
Sample (adjusted): 1991 2016
Included observations: 26 after adjustments
Variable
Coefficient
Std. Error
t-Statistic
Prob.
D(S&P500)
7.462409
0.547276
13.63555
0.0000
ET(-1)
-0.472095
0.162395
-2.907086
0.0077
R-squared
0.864669
Mean dependent var
658.8054
Adjusted R-squared
0.859030
S.D. dependent var
1531.309
S.E. of regression
574.9452
Akaike info criterion
15.62023
Sum squared resid
7933487.
Schwarz criterion
15.71701
Log likelihood
-201.0630
Hannan-Quinn criter.
15.64810
Durbin-Watson stat
2.220201
Appendix 12.
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