Sample entropy is a nonlinear method to measure the complexity of time series and widely applied in various fields. However, studies have shown that the entropy is not always related to the complexity of time series. To solve this problem, multi-scale entropy is proposed to measure the complexity of time series over different scales. However, considering that this method does not solve the problem of sample entropy in measuring the complexity of time series, a modified sample entropy based on time dependent is proposed and applied in the stock closing price and volume time series to study their corresponding complexity relations. At the same time, combined with multi-scale method, the complexity of closing time series and volume time series is measured over different scales. The experiment shows that the complexity of the closing price time series and volume time series can reveal a certain rule of stock development. In addition, the closing price sequence can maintain consistency on different scales, while the entropy value changes of the volume sequence at different scales have different trends, and the closer the stock type is, the closer the entropy change curve is.%样本熵是一个度量时间序列复杂度的非线性方法,广泛应用于各领域.然而,研究表明熵值的大小并不总是和时间序列的复杂性相关.为了解决这个问题,提出了多尺度熵,用来度量不同尺度下的时间序列的复杂度.但是,考虑到这种方法并没有解决样本熵在度量时间序列复杂度的问题,提出了基于时间依赖的改进样本熵,并将其用在股票收盘价和成交量时间序列上,研究它们对应的复杂度关系.同时,结合多尺度的方法,衡量不同尺度下股票收盘价时间序列和成交量时间序列的复杂性.实验结果表明,从收盘价时间序列和成交量时间序列的复杂度变化上能够揭示一定的股票的发展规律.另外,收盘价序列在不同的尺度上能够保持一致性,而成交量序列在不同的尺度上熵值变化则有不同的趋势,且股票类型越接近,熵值变化曲线也越接近.
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