| In nearly half a century, the integration of world capital market continues to deepen and empirical research on the integration of capital markets mushrooms, which are on behalf of the stock market. The stock markets are the central parts in world's long-term capital markets. The main characteristics of the stock markets and in particular, the correlation, transmission and periodicity between the stock markets have gained more and more attention in academic sphere.Integration of capital markets has an important meaning: the assets in different countries, which have similar risks, should have more or less the same incomes. After linking this phenomenon with the stock market, we find that as long as the domestic market is not entirely related to other countries, then investors should diversify investment between the countries. With the openness of national capital market and the strengthening of international capital flows, the dependency of the market is on the rise, the characteristics of the integration are more obvious and developed countries show significant linkage.The study of the dependency between the stock market, integration trends and the transmission problems plays an important guiding role in the investment portfolio of the international stock market. Since the 20th century, using statistical methods, in particular, time series analysis to study economic and financial time series is more and more popular. Since the time series methods have existed, there have been two methods which can observe analyze and interpret time series. The first is analyzing the data directly, namely the so-called time-domain analysis, through covariance function and differential equations. Co-integration is a typical time-domain analysis. Another method is to view time series as superposition of different harmonics and study the structural characteristics of a time-series in the frequency domain. It is called frequency analysis or spectrum analysis, through Fourier transform and spectral density function. These two approaches complement each other from different sides in different ways.As a result, on a basis of law of one price and risk-benefit ratio, this article uses time-domain analysis and frequency domain analysis as important tools to study common relevance, transmission and characteristics and improve the investment portfolio theory. The general comments include:(1) This thesis provides a summary of literatures concerning world capital market integration, dependency between international stock markets as well as the characteristics of the interaction. We also explore a variety of research methods and compare their advantages through a more comprehensive overview, spectral analysis and frequency domain analysis. This thesis also suggests that we should set up a framework of time-domain analysis and frequency domain analysis; therefore we can study correlation between the stock market, periodicity and transmission of international stock market. As a result of that, we can combine the merits of time-domain analysis and frequency domain analysis and overcome their limitations.(2) This thesis discusses theoretical foundation of the combination of time-domain analysis and frequency domain analysis in studying relevance and transmission of the stock market. When the stock market is relatively perfect, it is possible for it to give full play to allocation of resources, which can promote the process of financial globalization. An important theory of capital market integration is the "Law of One Price" or PPP assumption and it also can accounts for linkage of the stock markets. Similar assets in different countries, which have the same risks, should have more or less the same income. Portfolio theory focuses on the diversification of financial assets and it also bases on the principle of risk-benefit ratio, which can link the stock markets in countries. Capital market integration and transmission can be treated as an important part of portfolio investment theory. As a result, the combination of time-domain analysis and frequency domain analysis has become theoretical basis and research tools for studying the relevance, transmission and periodicity of stock markets.(3) This essay provides an empirical research basing on time-domain analysis of the stock market index as well as the industry index. Tanking advantage of Granger causality analysis, the co-integration and error correction model, we select more comprehensive samples, which can reflect the world's major stock markets, such as the U.S. Standard & Poor's 500 index, the British FTSE 100 index, Hong Kong's Hang Seng Index constituent stocks, Japan's Nikkei 225 index, as well as Chinese Shanghai Composite index. We also establish an empirical model and analyze long-run equilibrium relationship and short-term fluctuations between China and the major developed countries or regions. At the same time, based on the Global Industry Classification System (GICS) guidelines, this article choose CITIC and the S & P Europe 300 index, Japan, Britain, U.S. stock market Index for comparison, including energy, financial, industrial, basic materials and industries index, which can further explore the long-run equilibrium relationship and the short-term fluctuations between different countries or regions.(4)This essay provides an empirical research on the stock market index and industry index through spectral analysis method. Based on cross-spectrum analysis, we research and compare the various components of the cycle changes in the time series, revealing the structure of the frequency domain and mastering the volatility of the stock market index. Combined with the research on the cycle fluctuations of index time series, we further explore the direction, time and degree of strength of the transmission.This paper shows that:(1) In the long-term capital markets of all major countries, the stock market is most important. Because of the close political ties and economic relations, as well as more and more frequent international capital flows, mutual dependency of stock market of various countries and regions is also changing, and showed significant linkage characteristics in developed countries. The relevance of the market, cyclical and transmission characteristics had gradually become the focus of attention.(2) The time series analysis methods have two types, one is the direct analysis of the data's time characteristics (time-domain analysis), and the other is the analysis of the data's frequency characteristics (frequency spectrum analysis). Two approaches complemented each other and depicted the time series features from different sides in different ways.(3) This essay provides an empirical research basing on time-domain analysis of the stock market index as well as the industry index. Tanking advantage of Granger causality analysis, the co-integration and error correction model, we select more comprehensive samples, which can reflect the world's major stock markets, such as the U.S. Standard & Poor's 500 index, the British FTSE 100 index, Hong Kong's Hang Seng Index constituent stocks, Japan's Nikkei 225 index, as well as Chinese Shanghai Composite index. We also establish an empirical model and analyze long-run equilibrium relationship and short-term fluctuations between China and the major developed countries or regions. At the same time, based on the Global Industry Classification System (GICS) guidelines, this article choose CITIC and the S & P Europe 300 index, Japan, Britain, U.S. stock market Index for comparison, including energy, financial, industrial, basic materials and industries index, which can further explore the long-run equilibrium relationship and the short-term fluctuations between different countries or regions.(4)This essay provides an empirical research on the stock market index and industry index through spectral analysis method. Based on cross-spectrum analysis, we research and compare the various components of the cycle changes in the time series, revealing the structure of the frequency domain and mastering the volatility of the stock market index. Combined with the research on the cycle fluctuations of index time series, we further explore the direction, time and degree of strength of the transmission.(5) For the stock market index data, the use of cross-spectrum analysis conducted by the Research Positive results showed that: China's stock market index and Hong Kong's stock market index greater consistency. China's stock market index in the short-period lead for the performance of Hong Kong, Japan, the stock market index, Britain lags behind the stock market index, and in the long-period performance lags behind Hong Kong, Japan, the stock market index, ahead of the UK stock market index. Both the short-period or long period, the U.S. stock market index were significantly ahead of China's stock market index. However, with the longer period, the stock market between the two countries gradually phase 0, show that lead / lag relationship gradually weakened, that is, the synchronization of the two markets in the enhanced.Hong Kong, Japan, Britain and the United States stock market index between consistency and significantly greater than China's stock market index consistency, in which Britain and the U.S. stock markets are among the greatest consistency. Cycle from the point of view, Hong Kong, Japan, Britain and the United States stock market index of consistency between the long-period short period of consistency, the stock market index between the various countries show that there is a big long-term correlation characteristics. Hong Kong and Japan, Hong Kong and the United Kingdom, Japan and the United States, Britain and the United States stock market index consistency between the peaks in the long-period, respectively 82, 55, 35.4, 82 days. Hong Kong and the United States, Japan and the UK stock market index consistency between the peaks in a relatively short period, respectively 9.5,12 days. Accompanied by a short cycle length, as well as to the consistency of the increase in Hong Kong, Japan, Britain and the United States stock market index between the phases of the show were narrowed to the trend of 0, indicating that stock markets are among the countries in the long-standing significant synchronization, That is, to show common long-term trend.(6) For the stock market index, cross-spectrum analysis: China's stock market index of the financial industry and the European Union, Japan, Britain, the United States stock market, the financial sector index is greater than the coherence of energy, basic materials and industrial sectors between the index The consistency of the world's financial sector index showed greater relevance. From the analysis phase, the European Union, Japan, Britain, the United States stock market indexes are leading the industry in the Chinese stock market index trades.European Union, Japan, Britain and the United States stock market index between the various sectors of the greater consistency, and significantly greater than the energy industry with China's stock market index of consistency between the major developed countries that there is a big correlation characteristics. Various sectors between the index's performance for more short-period features, but the specific characteristics of the cycle, there are still some differences, and the formation of different investment and allocation strategy. Phase from the point of view, the industry index of synchronization between the characteristics of the more obvious to the general performance of the European Union and Britain ahead of Japan and the United States, the United States ahead of Japan.
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