Co-integration of stock markets in Europe In an age of rising globalization, the show of activities in intercontinental economic markets is an imperative issue for economic policy, especially in periods where markets are highly volatile. The determination of diversification strategies by an international investor also depends crucially on the nature and magnitude of the relationships existing between different stock markets. Thus it becomes important for international investors to understand the interrelations among the various markets to diversify risk and to derive high return.We can use co-integration to find out relationship between different stock markets of different countries. Co integration is a statistical property of time series variable. Two or more time series are co integrated if they share a common stochastic drift. If two or more series are individually integrated but some linear combination of them has a lower order of integration, then the series are said to be co integrated. Co-integration is a two step process: first any long run equilibrium relationships between exchange rates are established, and then a dynamic correlation model of exchange rate returns is estimated.This error correction model (ECM), so called because short term deviations from equilibrium are corrected, reveals the Granger causalities that must be present in a co integrated system. The fundamental aim of co-integration analysis is to detect any common stochastic trends in the price data, and to use these common trends for a dynamic analysis of correlation returns. Thus co-integration analysis is an extension of the simple correlation based analysis. Whereas correlation is based only on return data, co-integration analysis is based on the raw price, exchange rate or yield data as well as the return data.The study of co integration of stock markets is important because it is a direct consequence of globalization and it has important implications for investors. The combination of introduction of IT and globalization has significantly encouraged capital flows across national boundaries contributing to integration and co-integration of international stock markets. Our aim is to know whether there is co integration among stock exchange markets of major EU countries. Now a days stock market all over the world have become increasingly integrated and co-movement among major financial markets have been rising.Stock markets all over the world are changing frequently. European stocks markets are also changing. There are many European countries. They have their own stock markets. Here we want to find if there is any co integration among the major Europeans countries. Most of the European stock markets are important because the markets are full of opportunities. The main reason inducing us to focus on these countries is their joint membership in European union inferring great financial integration among them.Most of the European countries have the same economical structure. We will find out if there is any co-integration between the stock markets of We shall use the monthly data of stock exchange for the period of The methodology we will use. Literature Review A literature review is not an annotated bibliography in which you summarize briefly each article that you have reviewed. While a summary of what you have read is contained within the literature review, it goes well beyond merely summarizing professional literature.It focuses on a specific topic of interest to you and includes a critical analysis of the relationship among different works, and relating this research to your work. The Literature review develops a theoretical background for the study through a review of relevant theories. It means reviewing other peoples work on the same topic or similar topic. Subramanian (2008) examines co-integration and casual relations among five major stock exchanges in East Asia. He found out that price indices of the five countrieare co-integrated.Arshanapalli and Doukas [1993] use unit root and cointegration analyses to examine relationships and interactions among the stock markets of New York, Japan, Paris, Frankfurt, and London, from January 1980 to May 1990. The authors conclude that there has been an increasing interdependence among these stock markets after the crash of 1987, except for Japanese stock market. The French, UK, and German markets are significantly affected by the US market. The Japanese market performance has no links at all with any market in the US, France, Germany, and UK.Erdinc & Milla (2009) they assessed if there is co-integration among stock exchange markets of a bloc of major European countries of France, Germany and UK. They used unit root test and co-integration tests. From the result they found out that there are long term relationship when European countries are matched with each other. Koutmos [1996] finds evidence that the stock markets of France, Germany, Italy, and the UK are integrated because they are affected not only by local news, but also by international news, especially unfavorable, stemming from other markets.Friedman and Shachmurove [1997] also find that the larger markets of the EU comprising France, Germany, the Netherlands, and UK are highly related, but the smaller markets are more independent, implying larger benefits from short-run diversification by extending stock investment into those smaller countries. Moreover, the British stock market appears to be the leading market in the EU since it explains most of its own innovations and high proportions of the innovations in other markets.Al-Zalabani, Sagaran & Menon (2012) they conducted a research between Saudi stock market index (TASI) with leadind indices India, Chiana, Hong kong, Malaysia, USA and UK. They found out that Saudi stock market moves with American economic trends rather than with better performing markets. The research paper Johansen (1988) focused on using test to find out co-integration across various international stock markets. He compared the stock market index price of one country against that of the others. If the regression are stationary then the stock markets of the countries are co-integrated.The result forms the analysis were mixed. Nason and Watt (1994) showed, the power of the Johansen test falls sharply in the presence of a structural break. The Johansen test does not account for structural breaks in the stock market data, which can be caused by major political or economic events or policy changes. Hence, they might falsely signal the absence of cointegration in a system while actually it might be present. However, advances in the field of econometrics have refined the techniques toalso account for structural breaks in the data.Phengpis [2004] is an empirical analysis conducted upon stock price indices of five major EMU countries (France, Germany, Italy, the Netherlands, and Spain) , five non-EMU countries (Australia, Hong Kong, Japan, Singapore, and Switzerland), the US and UK for the period from January 1979 until June 2002. Unlike those of non-EMU countries, stock market price indices of the five EMU countries studied are cointegrated over the full sample period, over time, and even after controlling for the 1987 US stock market crash or the 1997 Asian financial crisis.Karim, Majid and A. Karim (2009) examined the stock market integration between Malaysia and its three largest trading partners i. e. , US, Japan and Singapore. For co-integration they used the ARDL approach. They found out that Malaysian stock market is integrated with the stock markets of US, Japan and Singapore. Since the examined stock markets are co-integrated, there exist a long term equilibrium relationship among them. All the research show that most of the Europeans countries are co-integrated with each other beacause they share the same characteristics.For example UK, France, Germany, Italy etc. They are co-integrated because they are members of European union. The Saudi stock market follows USA stock market style. They don’t follow China, Malaysia, Hong kong. Empirical Framework This article will concentrate on showing the co-integration among stock exchange of European countries and us stock market index. The European market will include Swiss market index, French market index, German market index and Italian market index and also us market indices.We will work with weekly stock index return of highest return and lowest return. But these raw data of stock index return is not valuable until there turned into data which bear logarithms. So, in this case the data of stock indices will be turned into a easier and more computable form of log which is Qt = log (Highest returnLowest return) First we will start with two unit root test to examine the co-integration test among these countries. A unit root is a feature of processes that evolve through time that can cause problems in statistical inference involving time series models.A linear stochastic process has a unit root if 1 is a root of the process’s characteristic equation. Such a process is non-stationary. If the other roots of the characteristic equation lie inside the unit circle — that is, have a modulus (absolute value) less than one — then the first difference of the process will be stationary. Consider a discrete time stochastic process {}, and suppose that it can be written as an autoregressive process of order p: ……………………………………………….. (1) Here, {} is a serially uncorrelated, mean zero stochastic process with constant variance . For convenience, assume .If is a root of the characteristic equation: ………………………………………………… (2) Then the stochastic process has a unit root or, alternatively, is integrated of order one, denoted If m = 1 is a root of multiplicity r, then the stochastic process is integrated of order r, denoted I(r). Then we will move to Phillips–Perron test which is is a unit root test. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1. It builds on the Dickey–Fuller test of the null hypothesis in ? , where ? is the first difference operator.Like the augmented Dickey–Fuller test, the Phillips–Perron test addresses the issue that the process generating data for might have a higher order of autocorrelation than is admitted in the test equation – making endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of ? as regressors in the test equation. Then we will run ADF test (augmented Dickey–Fuller test) which is a test for a unit root in a time series sample The testing procedure for the ADF test is the same as for the Dickey–Fuller test but it is applied to the model ………… (3) here is a constant, the coefficient on a time trend and the lag order of the autoregressive process. Imposing the constraints and corresponds to modelling a random walk and using the constraint corresponds to modelling a random walk with a drift. By including lags of the order p the ADF formulation allows for higher-order autoregressive processes. The unit root test is then carried out under the null hypothesis against the alternative hypothesis of Once a value for the test statistic It is computed it can be compared to the relevant critical value for the Dickey–Fuller Test.If the test statistic is less (this test is non symmetrical so we do not consider an absolute value) than (a larger negative) the critical value, then the null hypothesis of is rejected and no unit root is present. After that we will run Autocorrelation which is the cross-correlation of a signal with itself. Informally, it is the similarity between. In statistics, the autocorrelation of a random process describes the correlation between values of the process at different times, as a function of the two times or of the time difference.Let X be some repeatable process, and i be some point in time after the start of that process. (i may be an integer for a discrete-time process or a real number for a continuous-time process. ) Then Xi is the value (orrealization) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean? i and variance ? i2 for all times i. Then the definition of the autocorrelation between times s and t is ………………………………………………. (4) Where “E” is the expected value operator.Note that this expression is not well-defined for all time series or processes, because the variance may be zero (for a constant process) or infinite. If the function R is well-defined, its value must lie in the range [? 1, 1], with 1 indicating perfect correlation and ? 1 indicating perfect anti-correlation. If Xt is a second-order stationary process then the mean ? and the variance ? 2 are time-independent, and further the autocorrelation depends only on the difference between t and s.This further implies that the autocorrelation can be expressed as a function of the time-lag, and that this would be an even function of the lag ? = s ? t. This gives the more familiar form ………………………………………………………(5) and the fact that this is an even function can be stated as It is common practice in some disciplines, other than statistics and time series analysis, to drop the normalization by ? 2 and use the term “autocorrelation” interchangeably with “autocovariance” After that Johansen test will be run. In this test the null hypothesis for the trace test is the number of co integration vectors r ? , the null hypothesis for the eigenvalue test is r = ?. Just like a unit root test, there can be a constant term, a trend term, both, or neither in the model. For a general VAR(p) model: ……(6) Inferences are drawn on ? , and they will be the same, so is the explanatory power. Last but not the least we will run Granger causality test which is a statistical hypothesis test for determining whether one time series is useful in forecasting another. Ordinarily, regressions reflect “mere” correlations, but a certain set of tests reveal something about causality.Let y and x be stationary time series. To test the null hypothesis that x does not Granger-cause y, one first finds the proper lagged values of y to include in a univariate autoregression of y: ……………………. (7) Next, the autoregression is augmented by including lagged values of x: . (8) One retains in this regression all lagged values of x that are individually significant according to their t-statistics, provided that collectively they add explanatory power to the regression according to an F-test (whose null hypothesis is no explanatory power jointly added by the x’s).In the notation of the above augmented regression, p is the shortest, and q is the longest, lag length for which the lagged value of x is significant. these test will be developed in eviews, amos and similar softwares and the weekly data will be run through the these software to get accurate results which will show and explain the co-integration among these stock index data in the following table.