Abstract
Bitcoin, the first electronic payment system, is becoming a popular currency. We provide a statistical analysis of the log-returns of the exchange rate of Bitcoin versus the United States Dollar. Fifteen of the most popular parametric distributions in finance are fitted to the log-returns. The generalized hyperbolic distribution is shown to give the best fit. Predictions are given for future values of the exchange rate.
Highlights
Introduced and first documented by Satoshi Nakamoto in 2009, Bitcoin is a form of cryptocurrency—an “electronic payment system based on cryptographic proof” [1], instead of traditional trust. [1] noted that buying and selling online has become reliant “almost exclusively on financial institutions serving as trusted third parties to process electronic payments”
The generalized hyperbolic distribution gives the smallest values for −ln L, AIC, AICc, BIC, HQC, consistent Akaike information criterion (CAIC) and the largest p-values among all the five-parameter distributions
We have analyzed the exchange rate of Bitcoin versus United Stated Dollars (USDs) using fifteen of the most popular parametric distributions in finance, the most comprehensive collection of distributions ever fitted to any exchange rate data
Summary
Introduced and first documented by Satoshi Nakamoto in 2009, Bitcoin is a form of cryptocurrency—an “electronic payment system based on cryptographic proof” [1], instead of traditional trust. [1] noted that buying and selling online has become reliant “almost exclusively on financial institutions serving as trusted third parties to process electronic payments”. [1] noted that buying and selling online has become reliant “almost exclusively on financial institutions serving as trusted third parties to process electronic payments”. Payments for online transactions must go through a company, such as a bank or credit card issuer, to be checked for factors such as fraud and successful payment. This kind of system is based on trust, these checks come at a price in the form of increased transaction costs [1], meaning that we often see restrictions in the form of minimum spend limits for electronic payments—i.e., on credit or debit cards. The high liquidity, reduced costs and the high speed of Bitcoin’s partially anonymous system are what make this currency so interesting [3]
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