比特币与标准普尔 500 指数的静态比较分析

Yaoyue Tang, Karina Arias-Calluari, Michael S. Harré
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引用次数: 0

摘要

本文比较和对比了传统股票市场和加密货币之间的静态性。分析使用的数据集是 1996 年至 2023 年的标准普尔 500 指数盘中价格指数和 2019 年至 2023 年的比特币盘中指数,均以美元为单位。我们采用了 "广义敏感期 "的定义,该定义限制了时间序列的第一和第二矩的时间独立性。本文使用的检验方法遵循维纳-欣钦定理,即对于广义静止过程,功率谱密度和自相关是一对傅立叶变换。我们证明,可以通过将时间序列截断成段来实现局部静止,而对于每个段,都需要对价格回报进行去趋势和归一化处理。这些结果表明,在 12 个月的去趋势窗口和 10 分钟的限制归一化窗口下,S&P500 指数的价格收益率可以在整个 28 年期间实现静止。对于截断的分段,可以使用更大的归一化窗口来建立静态,这表明分段内的数据更加均匀。对于比特币价格回报率,波动性较高的分段在 60 分钟的归一化窗口下呈现出静态性,而其他分段则无法建立静态性。
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Comparative analysis of stationarity for Bitcoin and the S&P500
This paper compares and contrasts stationarity between the conventional stock market and cryptocurrency. The dataset used for the analysis is the intraday price indices of the S&P500 from 1996 to 2023 and the intraday Bitcoin indices from 2019 to 2023, both in USD. We adopt the definition of `wide sense stationary', which constrains the time independence of the first and second moments of a time series. The testing method used in this paper follows the Wiener-Khinchin Theorem, i.e., that for a wide sense stationary process, the power spectral density and the autocorrelation are a Fourier transform pair. We demonstrate that localized stationarity can be achieved by truncating the time series into segments, and for each segment, detrending and normalizing the price return are required. These results show that the S&P500 price return can achieve stationarity for the full 28-year period with a detrending window of 12 months and a constrained normalization window of 10 minutes. With truncated segments, a larger normalization window can be used to establish stationarity, indicating that within the segment the data is more homogeneous. For Bitcoin price return, the segment with higher volatility presents stationarity with a normalization window of 60 minutes, whereas stationarity cannot be established in other segments.
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