CO-INTEGRATION TESTING, USING THE JOHANSEN METHOD, BETWEEN GENERAL INDICATORS OF SOME ARAB FINANCIAL MARKETS IN ASIA
Tafila Technical University, College of Business, Jordan
ABSTRACT
The study aims to examine Co-integration by using the Johansen method between general indicators of some Arab Financial Markets in Asia. The study uses monthly data of the general indicators of stocks in Arab financial markets for the period from 2010-2017. In order to achieve the objectives of the study, the researcher examined the stationary of the indicators. In this regard, all indicators were found stable at the first difference. As a result, the data have met the first condition of co- integration investigation. The study found that the lag period is zero according to (schware) test. Moreover, the analysis of co- integration by testing the Co-integration Rank and the Maximum Eigen value showed the existence of one co- integration at least between Arab Financial Markets in Asia. The study provides a number of recommendations; the most important of which is to support more capital flows between the markets and to use attractive financial instruments for investors in the Arab Financial Markets in Asia. This can be done through the extensive use of Islamic financial instruments. Furthermore, the current paper aims at establishing a monetary integration between the study samples.
Keywords:Financial markets, Indicators, Financial markets, The Johansson co- integration, Stocks indicators.
ARTICLE HISTORY: Received:31 October 2018 Revised:5 December 2018 Accepted:2 January 2019 Published:28 January 2019.
Contribution/ Originality:The study aims to examine Co-integration by using the Johansen method between general indicators of some Arab Financial Markets in Asia.
Financial markets have largely developed through the flow of capitals among countries due to the important role of financial markets in dealing with investment decisions in countries, especially the Arab countries in Asia, which have relationships in finance and economics. The Co-integration of Arab countries, especially among the Gulf states in general and Jordan, comes to the convergence of geography and traditions, thus enhancing the flow of capital among the countries in question through the financial market, which is considered to be equipped for the investment decision in addition to the dependence of their economies on each other in addition to the movement of the capital, labor, goods exchanging and services. Arab countries seek to reduce transaction costs and legal restrictions to support financial and economic integration. Arab countries depend on each other's economies. Jordan is a major source of investment, especially for the Gulf States; (Saudi Arabia, Bahrain and the United Arab Emirates). The Gulf States in particular rely on Jordan for the sake of labor, as well as importing agricultural and industrial goods. This is the major reason that the research project comes through the use of the Johansson co-integration method in order to examine whether there is a co-integration between the major indicators of financial markets in Asia (Saudi Arabia, Bahrain, Abu Dhabi, Dubai and Jordan), which have economic, social, political and regional links. The research project covers monthly data for the period from 1/1/2010 to 31/12/2017. These data concern Arab major financial markets in Asia (Saudi Arabia, Bahrain, Abu Dhabi, and Dubai, Jordan). Data are also based on the general indices of monthly stock indicator in the Arab countries. The monthly data on all indicators and accessibility are available in addition to the growing financial and economic relations between the sample countries during this period.
The study will analyze the descriptive statistics of the research sample data. Moreover, it will analyze the relationship between the indicators of the research sample and then it will find out the co-integration through the first step in finding the stationary data. The second step is applying the deceleration period of the data. The third step is finding co- integration based on the slowdown period. Finally, results will be illustrated and later the recommendations of the study will be inferred and stated.
The problem of the research project comes from the use of the Johannes Co-integration test to examine whether or not there is a Co-integration of the major indicators of the Arab financial markets in Asia (Saudi Arabia Bahrain, Abu Dhabi, Dubai and Jordan) which have economic, social, political and regional linkage. Therefore, the problem of the study can be formulated through the following questions:
The study aims at achieving the following objectives:
The significance of this study is of a high value and benefit to the Arab and foreign investors in financial markets and investors in real investment. In addition, it is highly beneficial to researchers, students and decision makers who invest in the countries concerned. The results of the study are important to support the theoretical and practical aspects of the financial markets.
The study hypotheses can be formulated depending on the problem as follows-
There is a common integration between the Arab financial markets in the research sample that paves the way for the existence of a unified Arab financial market among all the other Arab countries through the following hypotheses.
There are several studies on the Co-integration of financial markets but very few of these studies tackled the precise idea of this research with its comprehensive study of the most Arab countries.
HandeErdincn (2009) conducted a study that aims at measuring the Co- integration of the stock markets at some of the main EU countries, France, Germany and the United Kingdom. The study is based on the market indicators of the European countries which (FTSE 100 Indicator, DAX Indicator, CAC4 Indicator, MSCI Indicator) 1 the study used the Johansen test of co- integration where there was a co-integration between the financial markets of the countries concerned due to the similarity of the economic structure in these countries.
Canarella et al. (2008) examine the Co-integration relationship between NAFTA's financial markets, (Canada, México and the United States), through the use of the Johansen test of Co- integration where the study showed an integration relationship between the market of Mexico and the United States of America.
Komlavi (2010) analyzed the Co-integration during the global financial crisis for the period from 2008 to August 2009 by analyzing the co-integration of international financial market indicators for Group of States (OECD Group, Pacific Group, Asia Group). The analysis shows that the three groups haveat least one co-integration relationship. This made investors in Asian capital markets never avoid any impact from financial markets, even if some domestic markets are still not fully open to the international market.
Muhammad and Syed (2012;2018) analyzed the determinants of the stock market between Pakistan and Asian economies from 2001 to 2015 by using Philips-Perron (PP) test to verify the co-integration of their financial markets. The results indicate that there is a long-term Co-integration between the Pakistan stock market and Stock markets in China, India, Indonesia, Korea, Malaysia and Thailand.
Neda and Amir (2014) examine the links between equity markets in five Asian countries; Malaysia, Indonesia, Philippines, Japan and Turkeywith United States of America. The study used monthly data for the period 1995-2010 through the use of VAR analysis. AR results showed significant market interactions. Moreover, the results showed that the US stocks are interconnected with all Asian stock markets. Furthermore, Japan is strongly intertwined with other Asian markets.
Mohamad and Wael (2013) conducted a study whose aim was to investigate the Co-integration of Arab financial markets mainly through focusing on previously defined countries; Kuwait and Jordan. The study used Johansen test of Co-integration. The study results showed a Co-integration relationship between the Kuwaiti and Jordanian financial markets.
However, there are many studies and research relevant to financial markets integration of countries that are not economically similar. The study of Walid (2008) examined long-term and dynamic relationships in the short term between the Egyptian Stock Exchange and its counterparts in the Group of Seven (G7). Results showed that the Egyptian stock exchange does not share long-term Co-integration relationships With G7.
Mohanasundaram and Karthikeyan (2015) explore the nature of the relationship among the stock market indices in South Africa, India and the USA. Their study used monthly data from stock indices, JALSH (South Africa), NIFTY (India) and NASDAQ (United States of America). Accordingly, the study led to a strong relationship among the stock market indices in South Africa, India and the United States of America.
Eventually, Mohamad and Wael (2013) examined the extent of Co-integration between EU countries and- Arab financial markets. Test results showed that the null hypothesis of non-integration cannot be accepted if the Arab market Indicator is a dependent variable. However, it can be accepted in the EU is a dependent Variable.
The financial market of Jordan is one of the oldest markets in the Arab world and was established in 1978. In 1989, the financial market in Bahrain was established and also started an active market in Saudi Arabia. In 2000, the Dubai Stock Exchange and the Abu Dhabi Stock Exchange were established in the United Arab Emirates (Ashraf, 2009).
The recent Arab financial markets are characterized by some common features, most notably the narrowness of the market. The tightness of the market in the Arab financial markets is due to the limited supply and demand of financial investment instruments in these markets, as well as the concentration of trading in a limited number of shares, The active shares traded to the total volume of trading, reflecting the small number of attractive shares, due to the concentration of some major investors to keep the shares of promising companies, in addition to the low quality of the majority of listed stocks as such the Arab financial markets are characterized by weak diversification of securities, poor liquidity and high volatility. This in turn leads to increased volatility in the profitability of the stock and consequently its market value, which raises fears among investors and presents them with high losses (Ashraf, 2009).
In this study will analyze the co- integration of financial markets in some Arab countries Where there are many benefits of co- integration between the financial markets of the countries of the region, the most important the management of local markets in an organized , efficient manner, the achievement of Found integration of financial institutions, markets and infrastructure together in the countries of financial integration also reduces the costs of financial intermediaries and increases competition because of the increasing number of financial institutions in the market, increasing financial services and increasing their contribution to growth also further financial development and efficiency, as integration leads to the elimination of financial imbalances and restrictions on the movement of capital In addition, the increase of foreign capital flows to the integration countries the larger and more liquid regional market may be more attractive to investors in international markets. Moreover, regional integration will allow financial institutions to diversify their resources better, reduce geographic and sectorial risks across companies and sectors, and improve the stability of financial systems in the average regional cost of capital and debt while at the same time providing opportunities for further risk reduction through diversification, and improvement inMarket liquidity and the availability of new investment instruments (Mark, 2007).
The concept of the general market indicator measures the level of indicator in the market, based on a sample of enterprises shares traded in regulated or unregulated capital markets or both. The sample is often selected in such a way as to allow the indicator to reflect the situation in which the capital market is intended to be measured (http://www.arabapi.org) .
In addition, the indicators are the value that measures the actual changes in the indicator of securities traded in the financial markets, using a mathematical equation that matches the nature of each financial market so as to identify the movement of indicator, trends and market performance. The main objective is to identify the movement of stock indicator in the financial market indicators of financial markets, during the years of study (Dredid, 2012).
The general indicators of stock indicator in the financial markets were based on the market trend and the study of the co- integration of financial markets; because they indicate the levels of stock indicator and determine indicator general price Stock price during a certain period, compared with another period (Shukairy and Saleh, 2012).
(TASI) is a digital standard which reflects changes in the market value of shares of all companies traded on Saudi stock market, and then it serves as a thermometer that measures the activity and prosperity of stock market (Ibrahim, 2005).
Figure (1) represents the Saudi Financial Market Indicator. (TASI), which reflects the trend of Saudi’s Financial Market Indicator during the study period for the monthly data during 2010-2017. It can be noted from the form that the trend of indicator in the market is raising at the beginning of the study until the summit reached in mid-2014.then the market trend began to decline and continued until it reached the bottom in the first third of 2016, as a result the market went in a bullish direction.
Figure-1. Saudi Financial Market Indicator.
Source: E-views program dependent on appendix (5)
Figure (2) Dubai Financial Market indicator (DFMGI) reflects the trend of Dubai’s Financial Market Indicator during the study period for the monthly data during 2010-2017. According to the form, it is notable that the trend of the indicator in the market is raising at the beginning of the study until it reaches the summit in mid of-2014, then the indicator began to decline and continued until it reaches the bottom in mid of-2015, followed by a gradual rise in indicator.
Figure-2. Dubai Financial Market Indicator (DFMGI)
Source: E- views program based on appendix (5)
Figure (3) represents Abu Dhabi’s Financial Market indicator (ADI). Which reflects the trend Abu Dhabi’s Financial Market Indicator during the study period for the monthly data for the period 2010-2017. It is noted from that the indicator trend in the market is raising at the beginning of the study until it reaches the summit in mid-2014, then the indicator begins to decline and continues until it reaches the bottom in mid-2015 then the market started to rise.
Figure-3. Abu Dhabi’s Indicator (ADI).
Source: E- views program based on appendix (5).
According to the form above, it is notable that the markets are moving according to Dow's technical analysis in the Saudi’s financial market, Dubai’s and Abu Dhabi’s Financial Market; indicating that the market is fluctuating then became stable based on Dow's theory in financial market (Dredid, 2012).
Figure (4) represents the general indicator of Bahrain’s Financial Market, which reflects the trend of the general Indicator of Bahrain Financial Market during the study period for the monthly data from 2010-2017. Based on the Figure, the indicator’s trend in the market begins to decline at the beginning of the study until it reaches the bottom at the end of 2012. Then the indicator inclines and continued until it reaches the summit at the third quarter of 2014, then the market declines until it reaches the bottom at the second quarter of 2016. In conclusion, the market started to rise one again.
Bahrain’s market is different from the other markets (Saudi Arabia, Dubai and Abu Dhabi) since the previous markets were having rising trends at the beginning of the study then they started to decline at the end of the study, while Bahrain market was at an opposite direction; it kept fluctuating between bearish trend and bullish trend at until the end of the study due to the fact that the financial markets are affected by economic events and investor movements among other financial markets.Figure-4. Bahrain Indicator (BAX)
Source: E- views program based on appendix (5)
Figure (5) represents Amman’s Financial Market Indicator (AMGNRLX), which reflects the trend Amman Financial Market Indicator during the study period. As the form shows price trend fluctuation in the market and began to decline at the beginning of the study until it reached the bottom in the third quarter of 2013. The indicator trend started to incline until it reaches the summit in the first quarter of 2014. The market kept fluctuating until the end of the study because financial markets are affected by political and economic events as well as by crises in neighboring countries and the whole region in general.
Jordanian market is different from the Saudi’s market, Dubai’s market and Abu Dhabi’s market. The previous markets were bullish at the beginning of the study, and then the markets declined at the end of the study, while Bahraini market was having the same position of the Jordanian market during the period of the study; whereas the markets were downward, then took the upward trend. The trend went downward at the end of the study because of the financial market is affected by political and economic events.
Figure-5. Amman’s Financial Market Indicator (AMGNRLX)
Source: E- views program based on appendix (5)
It’s notable from Appendix (1) that the highest values for the indicators were for the Saudi’s Indicator with (11112.12) points, while the lowest values for indicators were for Bahrain with (1048) points. According to the average price, as can be noticed from Appendix (4) that the highest average price for the Saudi’s Indicator was (7357.543) points while the lowest values was for the Bahrain’s Indicator of (1282.894) points. In addition, the standard deviation (risk) Saudi Indicator had the highest value but least for Abu Dhabi Indicator as for Skewness, all indicators have torsion on the right except Abu Dhabi’s Indicator that has negative torsion and fluctuations to the left, meaning that the indicators do not follow the normal distribution, confirmed by the (Jargue – Bera) test at level (a <0.05).
Table (1), shows a strong correlation between (ADI); the Indicator and the (DFMGI) Indicator Correlation has reached 98%, while the correlation (61%) was between the (TASI) and (AD I). In addition, the (71%) correlation was between (AMGN) and (BAX). Furthermore the value of correlation was (71%) between (TASI) and (DFMGI), but the remaining indicators have lower relations among them. As for (TASI) and (AMGN), it was negative due to the rise in the general Indicator of the Saudi’s stock indicator, reflecting the activity in the Saudi market and pointing to a decrease in the Jordanian market activity. Consequently, the decline in the indicator of Jordanian market is due to the Saudi’s investors and their movements in between the two markets.
Table-1. Expresses correlation between indicators in countries of study sample.
ADI |
AMGNRLX |
BAX |
DFMGI |
TASI |
|
ADI |
1 |
0.198382 |
0.980237 |
0.614469 |
|
AMGNRLX |
0.014515 |
0.014515 |
0.766862 |
0.018808 |
-0.10423 |
BAX |
0.198382 |
1 |
1 |
0.26829 |
0.365869 |
DFMGI |
0.980237 |
0.766862 |
0.26829 |
1 |
0.715017 |
TASI |
0.614469 |
0.018808 |
0.365869 |
0.715017 |
1 |
Source: E- views program based on appendix (5)
In order to find the Co-integration through the first step is to find out the stationary data, the second step is to apply a deceleration period of data whereas the third step is finding a Co integration as follows,
In order to calculate co- integration, all variables must be stable at the same level.
The rooted unit will be tested using the dickey fuller method in which the unit root is being applied. On other hand, all indicators of the study are found unstable, but they settle at the first difference. Appendix (2), shows that all variables are stabilized at the first difference. It’s necessary to achieve using Johansen co- integration.
The results of unit root test to be contained in the appendix (I). The Indicators; TASI, DFMGI, ADI , BAX , AMGNRLX are not stationary at any level ,but stationary at 1 %, 5%, and 10% level, with the first difference (d(1)); indicated by ADF results at all levels less than the critical values in negative direction. The ADF value for (TASI) is (-8.372111) and the critical values are (-2.589795) (-1.944286) and (-1.614487) at 1, 5, and 10 percent, respectively. The ADF value for (DFMGI) is (-10.33292) and the critical values are (-2.589795) (-1.944286) and (-1.614487) at 1, 5, and 10 %, respectively. The ADF value for (ADI) is-11.00283) and the critical values are (-2.589795) (-1.944286) and (-1.614487) at 1, 5, and 10 %, respectively. The ADF value for (BAX) is (-6.918654) and the critical values are (-2.589795) (1.944286) and (-1.614487) at 1, 5, and 10 %, respectively. The ADF value for (AMGNRLX) is (-10.05620) and the critical values are (-2.589795) (- 1.944286) and (-1.614487) at 1, 5, and 10 %, respectively.
It can be noticed from Appendix (3) the deceleration test (E-Views) values by using (summarize all 5 sets of assumption ) . Additionally, it can be noted that the deceleration period shows the lowest value selected in (linear intercept no trend model) because it is a better Model of Johansen co- integration. In addition, Appendix (2) shows that the deceleration period (zero) gives the lowest value when testing (Schwarz ( because it gives the best results among tests.
It can be noticed from Appendix (4) which shows that there is one Co-integration between the general indicators of stock indicator in financial markets of the country in Asia (the study sample). As shown in Appendix (4) unrestricted Co-integration Rank Test ( (Trace). Furthermore, it also can be noticed from Appendix (4) that confirms the results of) Unrestricted Co-integration Rank Test (Maximum Eigen value) which means there is a single Co-integration between the general indicators of stock indicator in the financial markets of the country in Asia (The study sample). Consequently , it’s been accepted that there is one Co -integration between general indicators of stock indicator in financial markets of the countries in Asia (The study sample), but rejects the hypothesis that there is more than co - integration between general indicators of stock indicator in financial markets of the country in Asia (The study sample).
By reviewing the previous studies where there were many studies on the integration of some of the financial markets However, the results of this study were different in addition to the difference in the study sample as follows
The main financial markets in the Arab countries in Asia have positive correlation between some of them. There is a positive relationship between Saudi Arabia and Dubai. There is also a positive correlation between Saudi Arabia and Abu Dhabi. Also, there is a positive relationship between Dubai and Abu Dhabi, and a positive relationship between Jordan and Bahrain. The analysis of Johansen Co-integration test showed that there is at least one Co-integration between financial markets (the sample of the study) by testing Trace Unrestricted Co-integration Rank Test (and Co-integration Rank Test (Maximum Eigen value.
The following study has come up with the following recommendations:
Funding: This study received no specific financial support. |
Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper. |
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Appendix (1)
ADI |
AMGNRLX |
BAX |
DFMGI |
TASI |
|||
Mean |
3703.766 |
2120.804 |
1282.894 |
2780.149 |
7357.543 |
||
Median |
4145.380 |
2119.450 |
1287.685 |
3074.385 |
7000.905 |
||
Maximum |
5253.410 |
2575.470 |
1591.940 |
5087.470 |
11112.12 |
||
Minimum |
2402.280 |
1850.590 |
1048.810 |
1353.390 |
5623.340 |
||
Std. Dev. |
944.7470 |
146.6717 |
137.3364 |
1119.480 |
1228.129 |
||
Skewness |
-0.14401 |
0.731302 |
0.103572 |
0.214465 |
1.150843 |
||
Kurtosis |
1.326896 |
3.920888 |
1.811977 |
1.792564 |
3.544155 |
||
Jarque-Bera |
11.52893 |
11.94899 |
5.817233 |
6.567531 |
22.37544 |
||
Probability |
0.003137 |
0.002543 |
0.054551 |
0.037487 |
|||
Sum |
355561.6 |
203597.2 |
123157.8 |
266894.3 |
706324.1 |
||
Sum Sq. Dev. |
84791949 |
2043697. |
1791823. |
1.19E+08 |
1.43E+08 |
||
Observations |
96 |
96 |
96 |
96 |
96 |
Appendix (2)
Null Hypothesis: TASI has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-0.06425 |
0.6588 |
||
Test critical values: |
1% level |
-2.58953 |
||
5% level |
-1.94425 |
|||
10% level |
-1.61451 |
*MacKinnon (1996) one-sided p-values
Null Hypothesis: D(TASI) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-8.37211 |
0.0000 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: DFMGI has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
0.185705 |
0.7380 |
||
Test critical values: |
1% level |
-2.58953 |
||
5% level |
-1.94425 |
|||
10% level |
-1.61451 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: D(DFMGI) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-10.3329 |
0.0000 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: ADI has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
0.746064 |
0.8738 |
||
Test critical values: |
1% level |
-2.58953 |
||
5% level |
-1.94425 |
|||
10% level |
-1.61451 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: D(ADI) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-11.0028 |
0.0000 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: BAX has a unit root
Exogenous: None
Lag Length: 1 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-0.61904 |
0.4467 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: D(BAX) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-6.91865 |
0.0000 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: AMGNRLX has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-0.98323 |
0.2895 |
||
Test critical values: |
1% level |
-2.58953 |
||
5% level |
-1.94425 |
|||
10% level |
-1.61451 |
*MacKinnon (1996) one-sided p-values.
Null Hypothesis: D(AMGNRLX) has a unit root
Exogenous: None
Lag Length: 0 (Automatic - based on SIC, maxlag=1)
t-Statistic |
Prob.* |
|||
Augmented Dickey-Fuller test statistic |
-10.0562 |
0.0000 |
||
Test critical values: |
1% level |
-2.5898 |
||
5% level |
-1.94429 |
|||
10% level |
-1.61449 |
Appendix (3)
Date: 09/01/18 Time: 18:23
Sample: 2010M01 2017M12
Included observations: 93
Series: ADI AMGNRLX BAX DFMGI TASI
Lags interval: 1 to 2
Selected (0.05 level*) Number of Cointegrating Relations by Model
Data Trend: |
None |
None |
Linear |
Linear |
Quadratic |
Test Type |
No Intercept |
Intercept |
Intercept |
Intercept |
Intercept |
No Trend |
No Trend |
No Trend |
Trend |
Trend |
|
Trace |
0 |
1 |
1 |
0 |
0 |
Max-Eig |
0 |
1 |
1 |
0 |
0 |
*Critical values based on MacKinnon et al. (1999)
Schwarz Criteria by Rank (rows) and Model (columns) |
|||||
0 |
62.30937* |
62.30937* |
62.51119 |
62.51119 |
62.69288 |
1 |
62.56349 |
62.46057 |
62.62281 |
62.66780 |
62.80112 |
2 |
62.88529 |
62.76390 |
62.88655 |
62.97848 |
63.07975 |
3 |
63.27838 |
63.16190 |
63.23582 |
63.35725 |
63.43249 |
4 |
63.71964 |
63.61892 |
63.66671 |
63.80374 |
63.83084 |
5 |
64.20660 |
64.10893 |
64.10893 |
64.28414 |
64.28414 |
Appendix (4)
Date: 08/28/18 Time: 22:11
Sample (adjusted): 2010M02 2017M12
Included observations: 95 after adjustments
Trend assumption: Linear deterministic trend
Series: ADI AMGNRLX BAX DFMGI TASI
Lags interval (in first differences): B0 to
Unrestricted Cointegration Rank Test (Trace)
Hypothesized |
Trace |
0.05 |
||
No. of CE(s) |
Eigenvalue |
Statistic |
Critical Value |
Prob.** |
None * |
0.308005 |
73.54019 |
69.81889 |
0.0245 |
At most 1 |
0.197686 |
38.56349 |
47.85613 |
0.2780 |
At most 2 |
0.101271 |
17.63927 |
29.79707 |
0.5928 |
At most 3 |
0.051763 |
7.495814 |
15.49471 |
0.5208 |
At most 4 |
0.025424 |
2.446521 |
3.841466 |
0.1178 |
Trace test indicates 1 co-integratingeqn(s) at the 0.05 level |
||||
* denotes rejection of the hypothesis at the 0.05 level |
||||
**MacKinnon et al. (1999) p-values |
||||
Unrestricted Co-integration Rank Test (Maximum Eigenvalue) |
||||
Hypothesized |
Max-Eigen |
0.05 |
||
No. of CE(s) |
Eigenvalue |
Statistic |
Critical Value |
Prob.** |
None * |
0.308005 |
34.97670 |
33.87687 |
0.0368 |
At most 1 |
0.197686 |
20.92422 |
27.58434 |
0.2808 |
At most 2 |
0.101271 |
10.14345 |
21.13162 |
0.7311 |
At most 3 |
0.051763 |
5.049293 |
14.26460 |
0.7356 |
At most 4 |
0.025424 |
2.446521 |
3.841466 |
0.1178 |
Max-eigenvalue test indicates 1 co-integratingeqn(s) at the 0.05 level
* denotes rejection of the hypothesis at the 0.05 level
**MacKinnon et al. (1999) p-values
Appendix (5)
obs |
ADI |
AMGNRLX |
BAX |
DFMGI |
TASI |
2010M01 |
2633.37 |
2525.1 |
1478.23 |
1589.97 |
6252.55 |
2010M02 |
2703.56 |
2470.88 |
1518.06 |
1592.91 |
6437.5 |
2010M03 |
2908.49 |
2517.72 |
1547.13 |
1843.47 |
6801.01 |
2010M04 |
2777.12 |
2575.47 |
1591.94 |
1739.88 |
6867.97 |
2010M05 |
2604.17 |
2401.57 |
1450.28 |
1579.54 |
6120.52 |
2010M06 |
2514.01 |
2348.56 |
1396.29 |
1461.8 |
6093.76 |
2010M07 |
2545.8 |
2334.77 |
1393.92 |
1512.4 |
6283.73 |
2010M08 |
2498.52 |
2249 |
1418.61 |
1483.67 |
6106.42 |
2010M09 |
2673.19 |
2306.46 |
1444.76 |
1683.69 |
6392.39 |
2010M10 |
2816.11 |
2335.61 |
1462.42 |
1764.54 |
6353.88 |
2010M11 |
2729.87 |
2354.6 |
1437.94 |
1668.82 |
6318.5 |
2010M12 |
2719.87 |
2373.58 |
1432.26 |
1630.52 |
6620.75 |
2011M01 |
2586.75 |
2373.78 |
1448.85 |
1534.4 |
6358.03 |
2011M02 |
2588.9 |
2251.73 |
1430.77 |
1410.7 |
5941.63 |
2011M03 |
2607.12 |
2175.59 |
1424.64 |
1556.04 |
6562.85 |
2011M04 |
2695.5 |
2198.01 |
1404.9 |
1634.13 |
6710.56 |
2011M05 |
2639.14 |
2159.83 |
1346.66 |
1559.92 |
6735.98 |
2011M06 |
2704.19 |
2093.52 |
1319.71 |
1516.93 |
6576 |
2011M07 |
2619.7 |
2082.8 |
1291.66 |
1517.58 |
6392.13 |
2011M08 |
2616.02 |
2036.43 |
1258.25 |
1492.44 |
5979.3 |
2011M09 |
2533.41 |
1991.6 |
1165.75 |
1431.71 |
6112.37 |
2011M10 |
2501.43 |
2018.15 |
1147.66 |
1408.06 |
6224.3 |
2011M11 |
2444.86 |
1964.22 |
1163.11 |
1378.94 |
6104.56 |
2011M12 |
2402.28 |
1995.13 |
1143.69 |
1353.39 |
6417.73 |
2012M01 |
2453.98 |
1946.61 |
1139.83 |
1435.72 |
6626.04 |
2012M02 |
2611.13 |
1959.75 |
1148.64 |
1730.43 |
7271.82 |
2012M03 |
2553 |
1990.4 |
1152.45 |
1648.87 |
7835.15 |
2012M04 |
2503.82 |
1981.2 |
1152.79 |
1630.95 |
7558.47 |
2012M05 |
2441.03 |
1874.5 |
1139.58 |
1471.49 |
6975.27 |
2012M06 |
2447.62 |
1882.07 |
1126.71 |
1451.87 |
6709.91 |
2012M07 |
2506.23 |
1852.48 |
1099.82 |
1542.64 |
6878.19 |
2012M08 |
2561.61 |
1923.95 |
1086.32 |
1547.82 |
7139.01 |
2012M09 |
2605.41 |
1902.68 |
1087.33 |
1578.79 |
6839.83 |
2012M10 |
2672.43 |
1917.87 |
1057.91 |
1619.61 |
6791.04 |
2012M11 |
2674.56 |
1929.28 |
1048.81 |
1607.9 |
6533.14 |
2012M12 |
2630.86 |
1957.6 |
1065.61 |
1622.53 |
6801.22 |
2013M01 |
2881.78 |
2045.73 |
1085.14 |
1887.59 |
7043.55 |
2013M02 |
3044.89 |
2042.42 |
1089.94 |
1927.1 |
6998.33 |
2013M03 |
3025.33 |
2101.36 |
1091.58 |
1829.24 |
7125.73 |
2013M04 |
3273.63 |
1998.13 |
1104.17 |
2135.4 |
7179.8 |
2013M05 |
3562.88 |
2017.47 |
1196.46 |
2366.79 |
7404.12 |
2013M06 |
3551.24 |
1980.53 |
1187.79 |
2222.57 |
7496.57 |
2013M07 |
3847.43 |
1956.52 |
1194.9 |
2588.53 |
7915.11 |
2013M08 |
3734.55 |
1874.96 |
1188.27 |
2523.13 |
7766.52 |
2013M09 |
3842.98 |
1850.59 |
1193.93 |
2762.5 |
7964.91 |
2013M10 |
3845.72 |
1969.34 |
1201.79 |
2922.18 |
8044.47 |
2013M11 |
3849.84 |
2022.63 |
1208.55 |
2945.91 |
8325.28 |
2013M12 |
4290.3 |
2065.83 |
1248.86 |
3369.81 |
8535.6 |
2014M01 |
4673.07 |
2206.96 |
1294.33 |
3770.38 |
8760.62 |
2014M02 |
4958.66 |
2178.17 |
1372.67 |
4220.45 |
9106.55 |
2014M03 |
4894.42 |
2148.93 |
1356.91 |
4451 |
9473.71 |
2014M04 |
5044.62 |
2124.15 |
1427.33 |
5058.95 |
9585.22 |
2014M05 |
5253.41 |
2130.92 |
1459.34 |
5087.47 |
9823.4 |
2014M06 |
4551.02 |
2113.03 |
1427.61 |
3942.82 |
9513.02 |
2014M07 |
4976.16 |
2136.57 |
1471.7 |
4833.24 |
10214.73 |
2014M08 |
5082.72 |
2131.91 |
1472.16 |
5062.96 |
11112.12 |
2014M09 |
5106.29 |
2114.98 |
1476.02 |
5042.92 |
10854.79 |
2014M10 |
4861.45 |
2106.13 |
1444.13 |
4545.39 |
10034.92 |
2014M11 |
4671.29 |
2132.49 |
1428.66 |
4281.43 |
8624.89 |
2014M12 |
4528.93 |
2165.46 |
1426.57 |
3774 |
8333.3 |
2015M01 |
4456.82 |
2169.61 |
1424.37 |
3674.4 |
8878.54 |
2015M02 |
4686.19 |
2195.46 |
1474.81 |
3864.67 |
9313.52 |
2015M03 |
4467.93 |
2135.43 |
1449.97 |
3514.4 |
8778.89 |
2015M04 |
4647.12 |
2115.53 |
1390.62 |
4229.04 |
9834.49 |
2015M05 |
4527.63 |
2183.57 |
1363.67 |
3923.24 |
9688.69 |
2015M06 |
4723.23 |
2115.64 |
1367.83 |
4086.83 |
9086.89 |
2015M07 |
4834.22 |
2125.72 |
1331.66 |
4143.21 |
9098.27 |
2015M08 |
4493.93 |
2097.59 |
1299.24 |
3662.56 |
7522.47 |
2015M09 |
4502.79 |
2045.23 |
1275.89 |
3593.28 |
7404.14 |
2015M10 |
4322.04 |
2034.42 |
1250.37 |
3503.75 |
7124.8 |
2015M11 |
4236.39 |
1993.72 |
1232.57 |
3204.28 |
7239.93 |
2015M12 |
4307.26 |
2136.32 |
1215.89 |
3151 |
6911.76 |
2016M01 |
4054.37 |
2147 |
1187.1 |
2997.77 |
5996.57 |
2016M02 |
4351.41 |
2116.25 |
1178.23 |
3239.7 |
6092.5 |
2016M03 |
4390.42 |
2151.89 |
1131.11 |
3355.53 |
6223.13 |
2016M04 |
4543.53 |
2094.72 |
1110.53 |
3491.91 |
6805.84 |
2016M05 |
4250.2 |
2118.44 |
1111.56 |
3313.72 |
6448.42 |
2016M06 |
4497.64 |
2091.35 |
1118.37 |
3311.1 |
6499.88 |
2016M07 |
4575.34 |
2102.13 |
1155.62 |
3484.32 |
6302.17 |
2016M08 |
4471.01 |
2076.83 |
1142.21 |
3504.4 |
6079.51 |
2016M09 |
4476.32 |
2120.46 |
1150 |
3474.38 |
5623.34 |
2016M10 |
4300.18 |
2107.58 |
1148.83 |
3332.41 |
6012.22 |
2016M11 |
4308.77 |
2170.98 |
1174.12 |
3360.91 |
7000.18 |
2016M12 |
4546.37 |
2170.29 |
1220.45 |
3530.88 |
7210.43 |
2017M01 |
4548.82 |
2161.47 |
1303.7 |
3642.85 |
7101.86 |
2017M02 |
4552.09 |
2212.76 |
1349.67 |
3630.34 |
6972.39 |
2017M03 |
4443.53 |
2250.18 |
1355.99 |
3480.43 |
7001.63 |
2017M04 |
4522.56 |
2185.26 |
1335.67 |
3414.93 |
7013.47 |
2017M05 |
4427.3 |
2175.18 |
1319.75 |
3339.37 |
6871.24 |
2017M06 |
4425.4 |
2167.4 |
1310.04 |
3392 |
7425.72 |
2017M07 |
4566.15 |
2139.82 |
1327.81 |
3633.18 |
7094.17 |
2017M08 |
4468.41 |
2157.26 |
1302.46 |
3637.55 |
7258.64 |
2017M09 |
4397.4 |
2121.52 |
1283.46 |
3563.99 |
7283.01 |
2017M10 |
4479.6 |
2093.19 |
1276.69 |
3635.87 |
6934.37 |
2017M11 |
4283.07 |
2122.47 |
1283.71 |
3420.17 |
7003.97 |
2017M12 |
4398.44 |
2126.78 |
1331.71 |
3370.07 |
7226.32 |
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