 # Chapter 1. Financial Markets, Prices and Risk (in R/Julia)

Copyright 2011 - 2022 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: https://www.gnu.org/licenses/.

##### Listing 1.1/1.2: Download S&P500 data in R Last updated August 2019

y=diff(log(price\$Index)) # calculate returns
plot(y)    # plot returns

##### Listing 1.1/1.2: Download S&P 500 data in Julia Last updated June 2022

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


##### Listing 1.3/1.4: Sample statistics in R Last updated July 2020

library(moments)
library(tseries)
mean(y)
sd(y)
min(y)
max(y)
skewness(y)
kurtosis(y)
jarque.bera.test(y)

##### Listing 1.3/1.4: Sample statistics in Julia Last updated July 2020

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))


##### Listing 1.5/1.6: ACF plots and the Ljung-Box test in R Last updated July 2020

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"))

##### Listing 1.5/1.6: ACF plots and the Ljung-Box test in Julia Last updated July 2020

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)


##### Listing 1.7/1.8: QQ plots in R Last updated June 2018

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

##### Listing 1.7/1.8: QQ plots in Julia Last updated July 2020

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: Download stock prices in R Last updated June 2018