Statistical analysis of switching states in stock market

这是对股票市场收益序列，特别是收益序列中长期波动的统计研究。在这项研究中，我们考察了收益率序列的均值是如何波动的，重点是上升趋势还是下降趋势。并利用统计模型确定了从向上(向下)到向下(向上)趋势阶段的转换点。利用收益率序列的平均周期行为与方差之间的关系，我们可以统计地识别股票市场的阶段。并对股票收益率序列中周期性行为的成因进行了研究。

This is the statistical research for stock market's return series, especially middle to long term fluctuations in the return series. In this research, we investigate how the mean of the return series fluctuates, focusing on upward or downward trend. And we identify the switching point from upward (downward) to downward (upward) trend phase using statistical models. Using the relationship between the mean cyclical behavior and variance in the return series, we can identify the stock market's phases as statistically. And we investigate causes of the cyclical behavior in the stock return series.