%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Matlab Beginning Practice
% Updated Spring 2021
% Copyright at Chaoyi Chen (BCE & MNB)
% All rights reserved. For use by registered students only.
% Please do NOT distribute without express written consent.
% Email: chaoyi.chen@uni-corvinus.hu
% Web: www.chenchaoyi.com
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% This exercises is intended to help you start learning Matlab
%%
% Getting started
% 1. Vector & matrix
x = [3 4 7 11]; % create a row vector (spaces)
b = [3;4;7;11]; % create a column vector (spaces)
length(x) % show the length of x
size(x) % show the size of x
z = x'; % ' means transpose so z is the transpose of x
n = zeros(5,1); % create a column vector with all elements = 0
nn = ones(1,5); % create a row vector with all elements = 1
y = eye(3); % create a 3 by 3 identity matrix
yy = inv(y); % create an inverse matrix of y; Another way is yy=y^(-1)

% 2. Display in the command line a text
disp('string can be added here'); % display a string
disp(y); % display a variable

% 3. Functions and plotting
x = 0:pi/100:2*pi; % pi=3.1415926....
y = sin(x); % y shows sin of x
plot(x,y) % plot(X,Y) creates a 2-D line plot of the data in Y versus the corresponding values in X.

% 4. For loop
s = 10;
h = zeros(10,1); 

for c = 1:s
    h(c) = c; % when c=1, h(1)=1; c=2, h(2)=2,..., c=10, h(10)=10
end  

%{
Sytax of for loop usually like:
for index = values
   statements
end
%}

%%
% Keeping warm up
% 1. Load data
load ADD YOUR DATASET NAME HERE % load mat. file
dataset = readtable('ADD YOUR FILE NAME HERE.csv'); % load csv. file and store data into dataset
DATAset = readtablexlsread('ADD YOUR FILE NAME HERE.xlsx','ADD THE SHEET NAME HERE'); % load one sheet in the xlsx. file and store data into DATAset

% 2. Matrix calculation
a = [1,2,3,4]; % a is 1 by 4
b = [2,3,4,5]; % b is 1 by 4
abprime = a*b'; % ab' is 1 by 1
aprimeb = a'*b; % a'b is 4 by 4

% 3. Simulate data
x = normrnd(0,1,100,1); %  generates a 100 by 1 vector such that each number is from the normal distribution with mean 0 and standard deviation 1.
e = normrnd(0,1,100,1);
y = 3*x+e; % y =3*x+e

% 4. OLS estimation
beta_ols = (x'*x)^(-1)*x'*y; % This is the OLS estimates of the coefficients
y_hat = x*beta_ols; % get 100 by 1 fitted value by OLS

% 5. Scatter plot and the fitted line
scatter(x, y) % scatter plot of (x,y)
hold on
plot(x, y_hat) % plot of fitted line
hold on
legend({ 'y', 'fitted y'}); % show legend
xlabel('x');
ylabel('y');
grid on 

%%
% The real challenge one (cross-sectional data)
% 1. generate a 100 by 1 vector of x by using x = rand(100,1);
% 2. generate a 100 by 1 vector of e by using e = normrnd(0,1,100,1);
% 3. let alpha = 1 and beta = 2;
% 4. generate y = alpha + beta*x + e;
% 5. regress y on x by using beta hat =(x'*x)^(-1)*x'*y;
% 6. collect the fitted y (say, y_hat);
% 7. plot the fitted line on the figure of data scatter

% The real challenge two (time series data)
% 1. let y = zeros(100,1);
% 2. let y(1) = normrnd(0,1);
% 3. let b = 0.5 & e = normrnd(0,1,100,1);
% 4. using the for loop to generate y(t) = 0.5*y(t-1)+e(t) 
% 5. estimate the model using ToEstMdl = arima(1,0,0); & [Est, ~, ~] = estimate(ToEstMdl, y, 'Display','off');
% 6. collect the residual by using resid = infer(Est,y);
% 7. plot the ACF figure via autocorr(resid)