As a project work, I looked at the dynamics of transactions in the Bitcoin cryptocurrency system. Delay times between consecutive payments were analysed to investigate their distribution - a distribution that could predict the next time an individual intends to spend money. This study is inspired by (Barabási 2005), a paper showing that human dynamics follow a fat-tailed power-law distribution in terms of certain tasks, like e-mail communication. It is yet to be examined if payment habits exhibit the same behavior or not. [Note: a fat-, or heavy-tailed distribution in this case is characterized by long waiting times, and burst like activities - e.g. we usually send e-mails in batches, time to time, and not in every hour a mail.]
Transactions, or payments, of 59490 accounts were fetched from the Bitcoin blockchain by calling the API of blockchain.info. Accounts were then filtered by the amount of payments initiated – minimum number of 60 transactions was required – in order to leave out bitcoin addresses used once (“Protect Your Privacy - Bitcoin” 2016) or just a few times. Account information of 6729 Bitcoin addresses made to the analysis phase in the end.
Inter-payment delay times of two accounts. Tall spikes suggests a heavy-tailed distribution - long waiting times (delay time in seconds).
Inter-payment delay times and transaction amounts were extracted from the account information. Delay times shorter than 10 minutes were filtered out, as the Bitcoin blockchain only stores the insertion time of blocks in the chain, which happens in every 10 minutes in average. Therefore, it is nonsense to analyse payment delays under such time period. In the end, 543273 transactions were examined. Complementary cumulative distribution of the delays was calculated and fitted to a power-law distribution (xmin=1617375, α=2.505).
I also intended to look at the correlation between delay times and amounts of Bitcoin paid for each transaction. I found no significant connection between the two variable.
Before cryptocurrency schemes became popular, investigation of global payment habits was not possible, as information of transactions was and is still kept private in the traditional banking system. Examination of the public Bitcoin blockchain concluded that between 1 day and almost a year (347 days) the distribution of inter-payment delay times clearly follow a power-law distribution with an exponent of -1.505. One more evidence for human processes being distributed in a heavy-tailed fashion in time deviating from the traditionally believed Poisson-like behaviour.
References
Barabási, Albert-László. 2005. “The Origin of Bursts and Heavy Tails in Human Dynamics.” Nature 435 (7039): 207–11. doi:10.1038/nature03459.
“Protect Your Privacy - Bitcoin.” 2016. Accessed January 26. https://bitcoin.org/en/protect-your-privacy.
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