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According to past research utilizing Bitcoin and other cryptocurrencies, Bitcoin has been shown to lead most other cryptocurrencies in terms of price movements. However, existing studies tend to focus on the direction of the lead-lag relationship instead of the duration of the lead-lag time. Furthermore, they are handicapped by the reliance on low-frequency data such as daily prices. This paper showcases the measurement of the lead-lag duration between cryptocurrencies using ultra-high-frequency tick-by-tick data, via the pair of Bitcoin and Cardano. Tick-by-tick data bring unique challenges in terms of methodology. The vast majority of time series econometrics methods are designed for use with data collected at regularly spaced time intervals, such as every hour, every day, etc. Tick-by-tick data, on the other hand, are not synchronized in any way and do not arrive at consistently spaced time intervals. Consequently, an asynchronous data integration methodology is utilized to estimate the Bitcoin price lead over Cardano price for each month beginning in January 2019 and continuing through May 2021. The length of the lead time ranges from 16 seconds to 118 seconds, with an average of around 57 seconds. Throughout the study period, the lengths of the lead time manifest a general trend of decline, which is shown to be statistically significant via non-parametric tests. Testing of seasonal patterns turns out to be not significant. The methodology and the findings of this paper have implications for both academics and practitioners, for example, when studying and implementing statistical arbitrage with cryptocurrencies.

There has been an extraordinary decrease in order execution time on stock exchanges in the past two decades. A related question is whether there has been a similar reduction in orders of magnitude for the lengths of the lead lag time between stocks. If the answer is affirmative, and the lengths of the lead lag time have long fallen below the human reaction time, algorithms have taken over information diffusion from one stock to another. Otherwise, humans continue to be in authority. In this study, the lengths of the lead lag time within pairs of stocks of large US companies are estimated using the Hayashi-Yoshida estimator, for each year from 2000 to 2022. We first construct stock pairs, with each pair containing two stocks from the same industrial sector. The median length of the lead lag time for each year shows a general trend of decline over time. From 2000 to 2005, the median lengths are a few seconds. By 2021 and 2022, they are less than 10 milliseconds. We also study a second construct in which stock pairs are randomly formed, but each pair contains stocks from two different sectors. The median length of the lead lag time for each year shows a decline over time, similar to the first construct. Overall, the lengths of the lead lag time in the second construct are not remarkably longer than those in the first construct. This shows that being in the same sector, at the tick-by-tick level, is not an important factor in determining the length of the lead lag time between stocks.