R and Julia Chapter 1. Financial Markets, Prices and Risk

# Chapter 1. Financial Markets, Prices and Risk

### R and Julia

Copyright 2011 - 2023 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: www.gnu.org/licenses.

##### Listing 1.1/1.2
price = read.csv('index.csv')
y=diff(log(price\$Index))  # calculate returns
plot(y)             # plot returns

##### Listing 1.1/1.2
using CSV
using DataFrames;
y = diff(log.(price[:,1]))
using Plots;
plot(y, title = "S&P500 returns", legend = false)


##### Sample statistics in R
library(moments)
library(tseries)
mean(y)
sd(y)
min(y)
max(y)
skewness(y)
kurtosis(y)
jarque.bera.test(y)

##### Sample statistics in Julia
using Statistics, StatsBase;
println("Standard deviation: ", std(y), "\n")
println("Minimum value: ", minimum(y), "\n")
println("Maximum value: ", maximum(y), "\n")
println("Skewness: ", skewness(y), "\n")
println("Kurtosis: ", kurtosis(y), "\n")
println("Autocorrelation of returns:", "\n", autocor(y, 1:20), "\n")
println("Autocorrelation of returns squared:", "\n", autocor(y.^2, 1:20), "\n")
using HypothesisTests;
println(JarqueBeraTest(y))
println(LjungBoxTest(y,20))
println(LjungBoxTest(y.^2, 20))


##### ACF plots and the Ljung-Box test in R
library(MASS)
library(stats)
par(mfrow=c(1,2), pty="s")
q = acf(y,20)
q1 = acf(y^2,20)
Box.test(y, lag = 20, type = c("Ljung-Box"))
Box.test(y^2, lag = 20, type = c("Ljung-Box"))

##### ACF plots and the Ljung-Box test in Julia
q1 = autocor(y, 1:20)
q2 = autocor(y.^2, 1:20)
plot(bar(q1, title = "ACF of returns"),
bar(q2, title = "ACF of returns squared"), legend = false)


##### QQ plots in R
library(car)
par(mfrow=c(1,2), pty="s")
qqPlot(y)
qqPlot(y,distribution="t",df=5)

##### QQ plots in Julia
using StatsPlots, Distributions;
plot(qqplot(Normal,float(y),qqline=:quantile, title = "QQPlot vs Normal"),
qqplot(TDist(5),float(y),qqline=:quantile, title = "QQPlot vs Student-t(5)"),
qqplot(TDist(4),float(y),qqline=:quantile, title = "QQPlot vs Student-t(4)"),
qqplot(TDist(3),float(y),qqline=:quantile, title = "QQPlot vs Student-t(3)"))


##### Listing 1.9/1.10
p = read.csv('stocks.csv')
y=apply(log(p),2,diff)
print(cor(y)) # correlation matrix

##### Listing 1.9/1.10
price = CSV.read("stocks.csv", DataFrame)