library(e1071) # skewness, kurtosis
library(NORMT3) 
library(VGAM) # Laplace
library(ADGofTest) # ad.test
library(fBasics) # dstable, stableFit -> levy

data <- read.csv("wig20_d.csv")

num_of_quotes <- nrow(data)

daily_changes <- log(data$Close[2:num_of_quotes]/data$Close[1:(num_of_quotes-1)])

par(mfrow=c(2,1))

plot(data$Close,type="l")
plot(daily_changes,type="l")

par(mfrow=c(1,1))

summary(daily_changes)
sd(daily_changes)

quantile(daily_changes)

quantile(daily_changes,c(0.001,0.01,0.05,0.95,0.99,0.999))

skewness(daily_changes)

kurtosis(daily_changes)

fitdistr(daily_changes,"normal")

mec <- mean(daily_changes)
sdc <- sd(daily_changes)

ad.test(daily_changes,pnorm,mec,sdc)

fitdistr(exp(mec+sdc*daily_changes),"lognormal")

(cauchy_fit <- fitdistr(daily_changes,"cauchy"))

cf_l <- cauchy_fit$estimate[1]
cf_s <- cauchy_fit$estimate[2]

ad.test(daily_changes,pcauchy,cf_l,cf_s)

laplace_fit <- vglm(daily_changes~1,laplace,data.frame(daily_changes),trace=TRUE,crot="l")
Coef(laplace_fit)

lf_l <- Coef(laplace_fit)[1]
lf_s <- Coef(laplace_fit)[2]

ad.test(daily_changes,plaplace,lf_l,lf_s)

(stable_fit <- stableFit(daily_changes))

sf_a <- stable_fit@fit$estimate[1]
sf_b <- stable_fit@fit$estimate[2]
sf_g <- stable_fit@fit$estimate[3]
sf_d <- stable_fit@fit$estimate[4]

ad.test(daily_changes,pstable,sf_a,sf_b,sf_g,sf_d)

stabledist::pstable(-0.1,sf_a,sf_b,sf_g,sf_d)  # probability of -10% or less
1-stabledist::pstable(0.1,sf_a,sf_b,sf_g,sf_d) # probability of +10% or more
stabledist::pstable(0.055,sf_a,sf_b,sf_g,sf_d)-stabledist::pstable(-0.055,sf_a,sf_b,sf_g,sf_d) # prob. of (-5.5%, +5.5%)

nd <- dnorm(x,mec,sdc)
cd <- dcauchy(x,cauchy_fit$estimate[1],cauchy_fit$estimate[2])
ld <- dlaplace(x,lf_l,lf_s)
sd <- stabledist::dstable(x,sf_a,sf_b,sf_g,sf_d)

plot(density(daily_changes),col="Black",ylim=c(0,max(nd,cd,ld,sd)),lwd=2)
curve(dnorm(x,mec,sdc),add=T,col="Green")
curve(dcauchy(x,cf_l,cf_s),add=T,col="Blue")
curve(dlaplace(x,lf_l,lf_s),add=T,col="Orange")
curve(stabledist::dstable(x,sf_a,sf_b,sf_g,sf_d),add=T,col="Red")

legend("left",c("black - Observed","green - Normal","blue - Cauchy","orange - Laplace","red - Stable"),fill=c("Black","Green","Blue","Orange","Red"))

http://reakkt.com

Analysis of the stock market daily returns distribution based on WIG20 index

R