Appendix - Introduction (in R/MATLAB)


Copyright 2011, 2016, 2018 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/.
The original 2011 R code will not fully work on a recent R because there have been some changes to libraries. The latest version of the Matlab code only uses functions from Matlab toolboxes.
The GARCH functionality in the econometric toolbox in Matlab is trying to be too clever, but can't deliver and could well be buggy. If you want to try that, here are the docs (estimate). Besides, it can only do univariate GARCH and so can't be used in Chapter 3. Kevin Sheppard's MFE toolbox is much better, while not as user friendly, it is much better written and is certainly more comprehensive. It can be downloaded here and the documentation here is quite detailed.


Listing R.1: Entering and Printing Data in R
Last updated June 2018

x = 10   # assign x the value 10
print(x) # print x
		
Listing M.1: Entering and Printing Data
Last updated June 2018

x = 10; % assign x the value 10, silencing output print with ;
disp(x) % display x
		

Listing R.2: Vectors, Matrices and Sequences in R
Last updated June 2018

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)
		
Listing M.2: Vectors, Matrices and Sequences
Last updated June 2018

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
		

Listing R.3: Importing Data in R
Last updated June 2018

## There are many data sources for financial data, for instance
## Yahoo Finance, AlphaVantage and Quandl. However, some of the
## free data sources have numerous issues with accuracy and
## handling of missing data, so only CSV importing is shown here.
##
## For csv data, one can use read.csv to read it
##
## Example:
## data = read.csv('Ch1aprices.csv', header=TRUE, sep=',')
## one can use the zoo() function from the package zoo
## to turn the data into a timeseries (see Listing 1.1/1.2)
		
Listing M.3: Importing Data
Last updated June 2018

%% There are many data sources for financial data, for instance
%% Yahoo Finance, AlphaVantage and Quandl. However, some of the
%% free data sources have numerous issues with accuracy and
%% handling of missing data, so only CSV importing is shown here.
%%
%% For csv data, one can use csvread to read it
%%
%% Example:
%% data = csvread('data.csv', 1, 0);
%% the two numbers behind are the row offset and column offset
%% so here we ignore the first row (ie. the header)
		

Listing R.4: Basic Summary Statistics in R
Last updated June 2018

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
		
Listing M.4: Basic Summary Statistics
Last updated June 2018

y = [3.14,15,9.26,5];
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
corrcoef(y)           % corr matrix = [1] for single vector
sort(y)               % sorting in ascending order
log(y)                % natural log
		

Listing R.5: Calculating Moments in R
Last updated June 2018

library(moments)
mean(y)          # mean
var(y)           # variance
sd(y)            # unbiased standard deviation, by default
skewness(y)      # skewness
kurtosis(y)      # kurtosis
		
Listing M.5: Calculating Moments
Last updated June 2018

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

Listing R.6: Basic Matrix Operations in R
Last updated June 2018

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
## Note: z * x is undefined since the two matrices are not conformable
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
## Note: dimensions must match along the combining axis
		
Listing M.6: Basic Matrix Operations
Last updated June 2018

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
%% Note: z * x is undefined since the two matrices are not conformable
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
%% Note: dimensions must match along the combining axis)
		

Listing R.7: Statistical Distributions in R
Last updated June 2018

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)
## Similar syntax for other distributions
## q for quantile, p for cdf, d for pdf
## followed by the abbreviation of the distribution
## One can also obtain pseudorandom samples from distributions
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
## Given data, we obtain MLE estimates of distribution parameters with package MASS:
library(MASS)
res = fitdistr(x, densfun = "normal")     # Fitting x to normal dist
print(res)
		
Listing M.7: Statistical Distributions
Last updated June 2018

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)
%% One can also obtain pseudorandom samples from distributions
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
%% Given sample data, we can also obtain MLE estimates of distribution parameters:
res = fitdist(x, "Normal") % Fitting x to normal dist
		

Listing R.8: Statistical Tests in R
Last updated June 2018

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
		
Listing M.8: Statistical Tests
Last updated June 2018

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
		

Listing R.9: Time Series in R
Last updated June 2018

x = rt(60, df = 5) # Create hypothetical dataset x
acf(x,20)          # autocorrelation for lags 1:20
pacf(x,20)         # partial autocorrelation for lags 1:20
		
Listing M.9: Time Series
Last updated June 2018

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
		

Listing R.10: Loops and Functions in R
Last updated June 2018

## For loops
for (i in 3:7)                             # iterates through [3,4,5,6,7]
    print(i^2)
## If-else loops
X = 10
if (X %% 3 == 0) {
    print("X is a multiple of 3")
} else {
    print("X is not a multiple of 3")
}
## Functions (example: a simple excess kurtosis function)
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)
		
Listing M.10: Loops and Functions
Last updated June 2018

%% For loops
for i = 3:7                          % iterates through [3,4,5,6,7]
    i^2
end
%% If-else loops
X = 10;
if (rem(X,3) == 0)
    disp("X is a multiple of 3")
else
    disp("X is not a multiple of 3")
end
%% Functions (example: a simple excess kurtosis function)
%% NOTE: in MATLAB, functions can be defined in 2 locations:
%% 1) in a separate file (e.g. excess_kurtosis.m in this case) in the workspace
%% 2) in the same file as the rest of the code, BUT at the end of the file
%% function k = excess_kurtosis(x, excess)
%%     if nargin == 1                % if there is only 1 argument
%%         excess = 3;               % set excess = 3
%%     end                           % this is how optional param excess is set
%%     m4 = mean((x-mean(x)).^4);
%%     k = m4/(std(x)^4) - excess;
%% end
		

Listing R.11: Basic Graphs in R
Last updated June 2018

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
		
Listing M.11: Basic Graphs
Last updated June 2018

y = normrnd(0, 1, 50, 1);
z = trnd(4, 50, 1);
subplot(2,2,1)
bar(y)                    % bar plot
subplot(2,2,2)
plot(y)                   % line plot
subplot(2,2,3)
histogram(y)              % histogram
subplot(2,2,4)
scatter(y,z)              % scatter plot
		

Listing R.12: Miscellaneous Useful Functions in R
Last updated June 2018

## Convert objects from one type to another with as.integer() etc
## To check type, use typeof(object)
x = 8.0
print(typeof(x))
x = as.integer(x)
print(typeof(x))
		
Listing M.12: Miscellaneous Useful Functions
Last updated June 2018

%% Convert objects from one type to another with int8() etc
%% To check type, use isfloat(object), isinteger(object) and so on
x = 8.0;
isfloat(x)
x = int8(x);
isinteger(x)