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Testing Bitcoins' Suceptibility To Financial Fraud

One of the first requirements for any monetary exchange is for it to have fraud enforcement measures. Does Bitcoin operate in a legitimate and credible monetary exchange? One can apply a classic fraud detection test that has been applied to countless amounts of political, financial, and natural data. It's called the Benford test, and we are going to be applying it to Bitcoin's overall historical prices. If the historical data passes the test, we can measure Bitcoins' ability to be tamper proof and consequently, part of a credible monetary exchange.

In 1938 a physicist named Dr. Frank Bedford articulated the probabilistic nature of naturally occurring sequences of numbers and analyzed their probability distribution. The data that he looked at consisted of 22,229 different sets, areas of rivers, buildings in the world by height, baseball statistics, and even stock prices. Using machines, he went on to count the frequency at which the first digit of each number appeared in his dataset. Below is an illustration of what he found:

Figure : Counting how frequent a data set starts with the number "d", where d ranges from 1 to 9.

This is the probability distribution of each digit. Notice that there are only 9 and not 10 digits. Zeroes are not counted in the Benford distribution, and so the next number is considered instead. Below is the distribution expressed as a function:

Figure : The Benford rate is shown in 4 different forms, all describing the same statistical distribution.

The above math simply expressed the same function in more than one way, but this is essentially what became known as Benford's law, or the first-digit law. It is a strong statement towards the nature of random, tamper-free sets of numbers to comport to a certain pattern, as long as they satisfy the following conditions:

• There were large datasets (to reduce noise)
• Number products, meaning results of multiple factors like price and quantity.
• Transaction level data like disbursements, sales, stock prices, etc.
• The data also is skewed towards the right, meaning that the mean is greater than the median.

Naturally occurring numbers that emerge from random stochastic processes follow a probabilistic pattern that has used the Benford rate as a benchmark to test the integrity and credibility of many types of data comporting to these conditions. Interestingly enough, stock prices can be plotted against this rate to test just how much of an emergent system they operate in. As Bitcoins gain credibility to operate as a legitimate monetary exchange system, I figured the behavior its historical prices would exhibit properties of an emergent system. Stochastic, efficient and "natural", precisely the sort of characteristics one would expect from a credible monetary exchange.

 Date Weighted Price 7/17/2010 0.05 … … 4/24/2013 143.19

Figure : The total historical prices of Bitcoins dating back to their inception in 2010. Source: Bitcoincharts.com

The "…" means the raw data for this exercise was in the thousands, and so had to be condensed. Below is another table that demonstrates our results:

 Number Sample Count Benford Rate Sample Rate 1 309 30.10% 30.69% 2 120 17.61% 11.92% 3 79 12.49% 7.85% 4 118 9.69% 11.72% 5 100 7.92% 9.93% 6 115 6.69% 11.42% 7 46 5.80% 4.57% 8 41 5.12% 4.07% 9 23 4.58% 2.28%

Figure : Out of a total of 1,007 daily Bitcoin prices, the table above shows the count of each data set that starts with the corresponding digit. This is why Benford's rate is called the first-digit law.

For the number 1, for example, there were 309 instances in which the first digit of the stated Bitcoinprice was a 1. Below is a graph merging both distributions:

Figure : Skewed to the right, with diminishing probabilities toward the left, both data sets have a 30% probability that the first digit will be a 1.

The good news is that visually, Bitcoin prices show that they follow the Benford trend, meaning that they pass the "tamper proof and fraud detection" test. Just in case there were skeptics out there thinking Bitcoins can be counterfeited like regular paper money, we can use tests like this to know when data is being artificially tampered with, and when it flows naturally. Now, does this correlation between the Benford rate and Bitcoin prices exhibit statistical significance? We ran an Excel linear regression test to find out. The caveat here is that the Benford rate maps a logarithmic function, but we are still going to see if there is any correlation whatsoever between the two, just to be sure.

 Slope 0.9032 .01633 intercept r-Squared 0.8454

The high r-Squared value gives us confidence is stating that Bitcoins' historical prices are as natural as the Benford rate. To many people who are wondering whether or not to put their savings in them, this should be very assuring. In this site there have already plenty of articles documenting the emergence of Bitcoins as an alternative currency, so check them out to get more background information on Bitcoins.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.