R and Matlab Appendix - Introduction

# Appendix - Introduction

### R and Matlab

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.

##### Entering and Printing Data in R
x = 10             # assign x the value 10
print(x)           # print x

##### % Entering and Printing Data
x = 10;             % assign x the value 10, silencing output print with ;
disp(x)             % display x


##### Vectors, Matrices and Sequences in R
y = c(1,3,5,7,9)          # create vector using c()
print(y)
print(y[3])               # calling 3rd element (R indices start at 1)
print(dim(y))             # gives NULL since y is a vector, not a matrix
print(length(y))          # as expected, y has length 5
v = matrix(nrow=2,ncol=3) # fill a 2 x 3 matrix with NaN values (default)
print(dim(v))             # as expected, v is size (2,3)
w = matrix(c(1,2,3),nrow=6,ncol=3) # repeats matrix twice by rows, thrice by columns
print(w)
s = 1:10                  # s is a list of integers from 1 to 10 inclusive
print(s)

##### % Vectors, Matrices and Sequences
y = [1,3,5,7,9]            % lists are denoted by square brackets
y(3)                       % calling 3rd element (MATLAB indices start at 1)
size(y)                    % shows that y is 1 x 5 (a row vector, by default)
length(y)                  % as expected, y has length 5
v = nan(2,3)               % fill a 2 x 3 matrix with NaN values
size(v)                    % as expected, v is size (2,3)
w = repmat([1,2,3]', 2, 3) % repeats matrix twice by rows, thrice by columns
s = 1:10                   % s is a list of integers from 1 to 10 inclusive


##### Basic Summary Statistics in R
y=matrix(c(3.1,4.15,9))
sum(y)         # sum of all elements of y
prod(y)        # product of all elements of y
max(y)         # maximum value of y
min(y)         # minimum value of y
range(y)       # min, max value of y
mean(y)        # arithmetic mean
median(y)      # median
var(y)         # variance
cov(y)         # covar matrix = variance for single vector
cor(y)         # corr matrix = [1] for single vector
sort(y)        # sorting in ascending order
log(y)         # natural log

##### % Basic Summary Statistics
y = [3.14; 15; 9.26; 5];    % List with semicolons is a column vector
sum(y)         % sum of all elements of y
prod(y)        % product of all elements of y
max(y)         % maximum value of y
min(y)         % minimum value of y
range(y)       % difference between max and min value of y
mean(y)        % arithmetic mean
median(y)      % median
var(y)         % variance
cov(y)         % covar matrix = variance for single vector
corrcoef(y)    % corr matrix = [1] for single vector
sort(y)        % sorting in ascending order
log(y)         % natural log


##### Calculating Moments in R
library(moments)
mean(y)      # mean
var(y)       # variance
sd(y)        # unbiased standard deviation, by default
skewness(y)  # skewness
kurtosis(y)  # kurtosis

##### % Calculating Moments
mean(y)      % mean
var(y)       % variance
std(y)       % unbiased standard deviation, by default
skewness(y)  % skewness
kurtosis(y)  % kurtosis


##### Basic Matrix Operations in R
z = matrix(c(1,2,3,4),2,2)   # z is a 2 x 2 matrix
x = matrix(c(1,2),1,2)       # x is a 1 x 2 matrix
z %*% t(x)                   # this evaluates to a 2 x 1 matrix
rbind(z,x)                   # "stacking" z and x vertically
cbind(z,t(x))                # "stacking z and x' horizontally

##### % Basic Matrix Operations
z = [1, 2; 3, 4]  % z is a 2 x 2 matrix (Note the use of ; as row separator)
x = [1, 2]        % x is a 1 x 2 matrix
z * x'            % this evaluates to a 2 x 1 matrix
vertcat(z,x)      % "stacking" z and x vertically
horzcat(z,x')     % "stacking z and x' horizontally


##### Statistical Distributions in R
q = seq(from = -3, to = 3, length = 7)     # specify a set of values
p = seq(from = 0.1, to = 0.9, length = 9)  # specify a set of probabilities
qnorm(p, mean = 0, sd = 1)                 # element-wise inverse Normal quantile
pt(q, df = 4)                              # element-wise cdf under Student-t(4)
dchisq(q, df = 2)                          # element-wise pdf under Chisq(2)
x = rt(100, df = 5)                        # Sampling 100 times from TDist with 5 df
y = rnorm(50, mean = 0, sd = 1)            # Sampling 50 times from a standard normal
library(MASS)
res = fitdistr(x, densfun = "normal")      # Fitting x to normal dist
print(res)

##### % Statistical Distributions
q = -3:1:3                       % specify a set of values
p = 0.1:0.1:0.9                  % specify a set of probabilities
norminv(p, 0, 1)                 % element-wise inverse Normal quantile
tcdf(q, 4)                       % element-wise cdf under Student-t(4)
chi2pdf(q, 2)                    % element-wise pdf under Chisq(2)
x = trnd(5, 100, 1);             % Sampling 100 times from t dist with 5 df
y = normrnd(0, 1, 100, 1);       % Sampling 50 times from a standard normal
res = fitdist(x, "Normal")       % Fitting x to normal dist


##### Statistical Tests in R
library(tseries)
x = rt(500, df = 5)                            # Create hypothetical dataset x
jarque.bera.test(x)                            # Jarque-Bera test for normality
Box.test(x, lag = 20, type = c("Ljung-Box"))   # Ljung-Box test for serial correlation

##### % Statistical Tests
x = trnd(5, 500, 1);                    % Create hypothetical dataset x
[h1, p1, jbstat] = jbtest(x)            % Jarque-Bera test for normality
[h2, p2, lbstat] = lbqtest(x,'lags',20) % Ljung-Box test for serial correlation - Needs Econometrics Toolbox


##### Time Series in R
x = rt(60, df = 5)  # Create hypothetical dataset x
par(mfrow=c(1,2), pty='s')
acf(x,20)           # autocorrelation for lags 1:20
pacf(x,20)          # partial autocorrelation for lags 1:20

##### % Time Series
x = trnd(5, 60, 1); % Create hypothetical dataset x
subplot(1,2,1)
autocorr(x, 20)     % autocorrelation for lags 1:20
subplot(1,2,2)
parcorr(x,20)       % partial autocorrelation for lags 1:20


##### Loops and Functions in R
for (i in 3:7)        # iterates through [3,4,5,6,7]
print(i^2)
X = 10
if (X %% 3 == 0) {
print("X is a multiple of 3")
} else {
print("X is not a multiple of 3")
}
excess_kurtosis = function(x, excess = 3){ # note: excess optional, default=3
m4 = mean((x-mean(x))^4)
excess_kurt = m4/(sd(x)^4) - excess
excess_kurt
}
x = rt(60, df = 5)                         # Create hypothetical dataset x
excess_kurtosis(x)

##### % Loops and Functions
for i = 3:7        % iterates through [3,4,5,6,7]
i^2
end
X = 10;
if (rem(X,3) == 0)
disp("X is a multiple of 3")
else
disp("X is not a multiple of 3")
end


##### Basic Graphs in R
y = rnorm(50, mean = 0, sd = 1)
par(mfrow=c(2,2)) # sets up space for subplots
barplot(y)        # bar plot
plot(y,type='l')  # line plot
hist(y)           # histogram
plot(y)           # scatter plot

##### % Basic Graphs
y = normrnd(0, 1, 50, 1);
z = trnd(4, 50, 1);
subplot(2,2,1)
bar(y)            % bar plot
title("Bar plot")
subplot(2,2,2)
plot(y)           % line plot
title("Line plot")
subplot(2,2,3)
histogram(y)      % histogram
title("Histogram")
subplot(2,2,4)
scatter(y,z)      % scatter plot
title("Scatter plot")


##### Miscellaneous Useful Functions in R
x = 8.0
print(typeof(x))
x = as.integer(x)
print(typeof(x))

##### % Miscellaneous Useful Functions
x = 8.0;
isfloat(x)
x = int8(x);
isinteger(x)


##### Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.