比特币与标普500收益率的跨尺度平稳性
文章 arXiv papers · 作者: Yaoyue Tang et al.
总结
本研究比较日内标普500与比特币价格收益率的广义平稳性。研究利用自相关与功率谱密度之间的关系检验平稳性，并考察分段、去趋势和归一化如何影响结果。标普500的数据时间跨度远长于比特币数据。
报告的发现表明，使用较长的去趋势窗口和较短的归一化窗口，可以使标普500收益率在整个样本中达到平稳；分段分析则允许使用较大的归一化窗口。对于比特币，报告称只有在波动率较高的区段使用较长归一化窗口时才呈现平稳性，其他区段则没有。这些结论取决于所选预处理方法、窗口、样本时期和平稳性定义；所提供的文本没有说明更广泛的稳健性检验，也未讨论对预测和交易的影响。
核心观点
- 研究将平稳性定义为一阶和二阶矩不随时间变化。
- 研究使用维纳—辛钦关系，即自相关与功率谱密度之间的关系，检验平稳性。
- 分段、去趋势和归一化会影响收益率是否呈现平稳性。
- 报告中的标普500与比特币结果有所不同，并受区段和预处理选择影响。
标签
全文
# Comparative analysis of stationarity for Bitcoin and the S&P500 # 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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