| In recent years,the government has been emphasizing the need to achieve stable economic growth by implementing countercyclical operations,which has driven scholars to study the cycles and fluctuations in the operation of various factors in the field of the market economy.Among them,the interactive effects and spillover effects of the cyclical fluctuations of stock prices and economic cycle fluctuations in financial markets have been the focus of research in finance.The China’s stock market has reached a market capitalization scale of more than 80 trillion yuan after 30 years of growth.Besides,its gross national product has increased by more than 20 times in the same period.However,China’s Shanghai Composite Index has basically hovered at more than 3000 points in the past decade.What is the relationship between China’s stock index,industry sector index and macroeconomic cycle?If there is a certain interaction between the price fluctuation cycle of China’s stock market and the macroeconomic fluctuation cycle,then promoting the development of the stock market can affect the macroeconomic development and cycle.In addition,market investors can predict stock prices and formulate investment strategies in line with periodic fluctuations according to the law of market fluctuations if the fluctuations of stock index and industry index follow a regular movement system in a period of time.Taking the theories related to the interaction mechanism of economic cycles and stock market price cycles as the basis is an essential premise to describe the relationship between economic cycle fluctuations and stock market price fluctuation cycles.The key to carrying out the empirical analysis is to extract the economic cycle and stock market price cycle.Previous studies on economic cycle to extract the cycling term generally use methods such as HP filter and BK filter,but these methods have to pre-set the filtering period first and have more strict requirements on the statistical distribution and smoothness of the original series.Therefore,this paper adopts the singular spectrum analysis method(SSA)to extract the respective reconstructed periodic terms and then study the interactive effects and leading-lag relationship between economic cycles and stock market price fluctuation cycles.SSA mainly extracts the effective information from the time series and decomposes it into different independent components,such as trend term,periodic term,and noise term,so as to further study and analyze the structure of the time series and make the extracted periodic terms more detailed and accurate.The main empirical research methods selected in this study are not only singular spectrum analysis,but also the emerging TVP-VAR spillover model analysis,Granger causality test in time domain,impulse response function analysis,analysis of variance and frequency domain spectrum analysis and so on for the empirical test of economic cycle and stock price fluctuation cycle.With these methods,this study makes an empirical test on the medium-and long-term economic cycle and the corresponding stock sector and index cycle of China,the United States,Japan and the United Kingdom.The test samples include:China’s medium-cycle Jugla cycle composite index and equipment manufacturing stock price volatility cycle composite index,China medium-and long-term Kuznets cycle composite index and real estate stock price volatility cycle composite index,China long-period Kondratiev cycle composite index and Shanghai Composite Index;American long-term Kondratiev cycle Composite Index and Dow Jones Index;UK medium-and long-term Kuznets cycle Composite Index and Real Estate Stock Price volatility cycle Composite Index;Japan medium-and long-term Kuznets cycle Composite Index and Real Estate Stock Price volatility cycle Composite Index,Japan long-term Kondratiev cycle Composite Index and Nikkei 225 Index.There is a long-term interaction between China’s mid-cycle Jugla cycle and the equipment manufacturing stock price fluctuation cycle under the empirical analysis.In addition,there is an obvious Granger causality between them in the short term.At the same time,the equipment manufacturing stock price fluctuation cycle under the singular spectrum reconstruction is 3-5 months ahead of the Jugla cycle,and the change of the former brings a positive response to the latter.Empirical analysis shows that there is a long-term correlation between the medium-and long-term Kuznets cycle and the real estate stock price fluctuation cycle in China,Britain and Japan,and between the long-term Kondratiev cycle and the stock price index fluctuation cycle in China,the United States and Japan.However,there are differences in the empirical results such as Granger causality and spectral analysis,and the running rhythm is not completely consistent among the cycles of various countries.The main reason for the difference is the market maturity and the different economic history and economic policies of specific industries in different countries.Combined with the autoregressive moving average forecasting model,this study forecasts the future trend of different industry sectors and index cycle respectively under the relevant empirical evidence.According to dynamic spillover effect analysis,there is a two-way spillover relationship between China’s Jugla cycle and China’s equipment manufacturing stock price fluctuation cycle,China-UK-Jap an Kuznets cycle and real estate stock price fluctuation cycle,China-Japan-US Kondratieff wave and stock price index fluctuation cycle,and the extreme value of the spillover index all appears in the "crisis period".That is,the spillover index of"turbulent period" is greater than that of "stationary period".Comparing the volatility spillover between the Kuznets cycle and the real estate stock price fluctuation cycle in China,Britain and Japan,the volatility range of the composite spillover index of China and Japan is lower than that of the United Kingdom in most of the time;compared with the volatility spillover between the Kondratieff wave and the stock price index fluctuation cycle of China,Japan and the United States,the volatility range of the composite spillover index of the United States and Japan is lower than that of China in most of the time.This study makes an empirical study on the interaction and spillover effects between economic cycle and stock market volatility.In addition,it makes a quantitative analysis of the relevant economic cycle and stock market interaction.It can provide a reference basis for the government to subdivide the industry when formulating countercyclical policies,deepen the academic understanding of the dynamic relationship between the two areas,and better regulate the two-way development of the stock market and the economy.In the meanwhile,it provides a reference for investors to adjust their long-term investment strategies,optimize their portfolios and improve their investment returns. 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