Bitcoin price and Benford's law

The first digit of numbers often follow Benford's law. Manipulation of those numbers by humans can be detected via corresponding statistic tests since humans cannot produce numbers following the needed distribution(s) (except they use a computer and know, that the original data follows Benford's law):

https://en.wikipedia.org/wiki/Benford%27s_law
https://en.wikipedia.org/wiki/Benford%27s_law#Price_digit_analysis

Now something to think about and to discuss (but maybe I used the following tools wrongly):

Some R:
https://www.rdocumentation.org/packages/benford.analysis/versions/0.1.5

Code:

library(anytime); # für Zeitumrechnung
library(benford.analysis); # für Benford

temp <- tempfile();
download.file("https://api.bitcoincharts.com/v1/csv/bitstampUSD.csv.gz", temp);
table <- read.csv(gzfile(temp));
unlink(temp);

rm(temp);
gc();

# Benennung der Spalten
colnames(table) <- c("EPOCH", "PRICE", "VOLUME");

# Anfügen einer neuen Spalten mit den Daten (Datums), da ansonsten Epochs
table <- cbind(table, "DATE"=anydate(table[,1], "CEST"));

x <- benford(table$PRICE);
plot(x);

y <- getSuspects(x, table);
#hist(as.Date(y$DATE), breaks=1000);
hist(as.Date(unique(y$DATE)), breaks=314)

z <- y[grepl("2019", y$DATE),];
unique(z$DATE);

Some results:

General distribution of bitstamp's price digits:

General statistics of data:

Code:

Benford object:
 
Data: table$PRICE 
Number of observations used = 34361833 
Number of obs. for second order = 1636552 
First digits analysed = 2

Mantissa: 

   Statistic Value
        Mean  0.58
         Var  0.10
 Ex.Kurtosis -1.19
    Skewness -0.46


The 5 largest deviations: 

  digits absolute.diff
1     10      820554.5
2     20      604793.2
3     19      575172.8
4     11      574876.8
5     18      561510.5

Stats:

	Pearson's Chi-squared test

data:  table$PRICE
X-squared = 11178000, df = 89, p-value < 2.2e-16


	Mantissa Arc Test

data:  table$PRICE
L2 = 0.090839, df = 2, p-value < 2.2e-16

Mean Absolute Deviation (MAD): 0.005221502
MAD Conformity - Nigrini (2012): Nonconformity
Distortion Factor: 21.44937

Time points where price digits do not follow Benford's law:

The corresponding time points for 2019 (note the date, when this started and when it ended!):

Code:

 [1] "2019-06-21" "2019-06-22" "2019-06-23" "2019-06-24" "2019-06-27"
 [6] "2019-06-28" "2019-06-30" "2019-07-01" "2019-07-02" "2019-07-03"
[11] "2019-07-05" "2019-07-06" "2019-07-11" "2019-07-13" "2019-07-14"
[16] "2019-07-15" "2019-07-16" "2019-07-18" "2019-07-19" "2019-07-20"
[21] "2019-07-21" "2019-07-22" "2019-07-23" "2019-07-25" "2019-07-27"
[26] "2019-07-31" "2019-08-01" "2019-08-02" "2019-08-03" "2019-08-04"
[31] "2019-08-05" "2019-08-13" "2019-08-14" "2019-08-15" "2019-08-16"
[36] "2019-08-17" "2019-08-18" "2019-08-19" "2019-08-20" "2019-08-21"
[41] "2019-08-22" "2019-08-23" "2019-08-24" "2019-08-25" "2019-08-26"
[46] "2019-08-27" "2019-08-28" "2019-09-02" "2019-09-03" "2019-09-04"
[51] "2019-09-05" "2019-09-06" "2019-09-07" "2019-09-08" "2019-09-09"
[56] "2019-09-10" "2019-09-11" "2019-09-12" "2019-09-13" "2019-09-14"
[61] "2019-09-15" "2019-09-16" "2019-09-17" "2019-09-18" "2019-09-19"
[66] "2019-09-20" "2019-09-21" "2019-09-22" "2019-09-23"

References: https://bitcointalk.org/index.php?topic=26136.msg52592024#msg52592024