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
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$DATE);
Some results:
General distribution of bitstamp's price digits:
General statistics of data:
Benford object:
Data: table$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!):
[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://bitcointalksearch.org/topic/m.52592024