Abstract This study examines time–frequency relationship between Bitcoin prices and Bitcoin mining based on daily data from January 2013 to October 2018. Bitcoin mining is measured through Bitcoin hashrate, which represents the completion speed of the Bitcoin code. We also include three energy commodities, i.e. oil, coal, and gas in a multivariate model employing time–frequency wavelet extensions in the form of partial and multivariate models. Results of our study suggest that both oil and gas lead Bitcoin returns from mid 2014 till 2016 across 64– 128 days' period. Under the investment period of 64– 256, hashrate and Bitcoin returns share significant comovement in the presence of oil and natural gas however exhibit no comovement when the effect of coal market is considered. Our results of wavelet decomposition suggest that the magnitude of comovement ranging from short- to long-run is time varying. Finally, results of the causality on quantile test suggest that Bitcoin returns cause changes in Bitcoin hashrate mostly during median quantiles with an asymmetric pattern. Our work entail implications for investors in the Bitcoin and energy market and is also helpful in forecasting the pricing behavior of Bitcoin using the hashrate and vice versa.

中文翻译：

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比特币哈希率与能源商品市场之间的时频联动和因果关系

摘要该研究基于2013年1月至2018年10月的每日数据，研究了比特币价格与比特币开采之间的时间-频率关系。比特币开采是通过比特币哈希率来衡量的，它代表了比特币代码的完成速度。我们还使用时频小波扩展以部分模型和多元模型的形式，在多元模型中包括三种能源商品，即石油，煤炭和天然气。我们的研究结果表明，从2014年中到2016年，石油和天然气均领先于比特币64-128天的回报。在64-256的投资期限内，在存在石油和天然气的情况下，哈希率和比特币收益共享显着的联动，但是考虑到煤炭市场的影响，散列率和比特币的收益没有联动。我们的小波分解结果表明，从短期到长期的同动幅度是随时间变化的。最后，分位数测试的因果关系结果表明，比特币回报率主要在具有不对称模式的中位数分位数期间导致比特币哈希率发生变化。我们的工作对比特币和能源市场的投资者产生了影响，也有助于使用哈希率预测比特币的定价行为，反之亦然。