Yaoyue Tang, Karina Arias-Calluari, Michael S. Harré
{"title":"Comparative analysis of stationarity for Bitcoin and the S&P500","authors":"Yaoyue Tang, Karina Arias-Calluari, Michael S. Harré","doi":"arxiv-2408.02973","DOIUrl":null,"url":null,"abstract":"This paper compares and contrasts stationarity between the conventional stock\nmarket and cryptocurrency. The dataset used for the analysis is the intraday\nprice indices of the S&P500 from 1996 to 2023 and the intraday Bitcoin indices\nfrom 2019 to 2023, both in USD. We adopt the definition of `wide sense\nstationary', which constrains the time independence of the first and second\nmoments of a time series. The testing method used in this paper follows the\nWiener-Khinchin Theorem, i.e., that for a wide sense stationary process, the\npower spectral density and the autocorrelation are a Fourier transform pair. We\ndemonstrate that localized stationarity can be achieved by truncating the time\nseries into segments, and for each segment, detrending and normalizing the\nprice return are required. These results show that the S&P500 price return can\nachieve stationarity for the full 28-year period with a detrending window of 12\nmonths and a constrained normalization window of 10 minutes. With truncated\nsegments, a larger normalization window can be used to establish stationarity,\nindicating that within the segment the data is more homogeneous. For Bitcoin\nprice return, the segment with higher volatility presents stationarity with a\nnormalization window of 60 minutes, whereas stationarity cannot be established\nin other segments.","PeriodicalId":501139,"journal":{"name":"arXiv - QuantFin - Statistical Finance","volume":"39 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Statistical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02973","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.