% Karapatsias Vasileios (8155)
% Sismanis Michail (8242)
% Part B (non linear)
% Timeseries 2018-2019 , AUTh

%% Initialize the dataset
clc
clear all;
close all;
addpath('functions_non_linear/');
addpath('functions_linear/');


fprintf("Importing the dataset.\n");
dataset = importdata('dat11.dat');
dataLength = length(dataset);

fprintf("Resampling every 6th day. . .\n");
% myData = dataset(1:6:dataLength);
myData = resample(dataset,1,6);
dataLength = length(myData);

figure;
clf
plot(myData)
title('Initial Timeseries (cont)')
saveas(gcf,'partBb_figures/initial_contin.png')

figure;
plot(myData,'.','markersize',6)
title('Initial Timeseries (disc)')
saveas(gcf,'partBb_figures/initial_disc.png')

figure;
plot(myData)
hold on
plot(myData,'.','markersize',6)
title('Initial Timeseries (both)')
saveas(gcf,'partBb_figures/initial_both.png')

% Initial autocorrelation
Maxtau = 100;
alpha = 0.05;
zalpha = norminv(1-alpha/2);
autlim = zalpha/sqrt(dataLength);

figure;
initialAutocorr = autocorrelation(myData, Maxtau,'Initial ');
saveas(gcf,sprintf('partBb_figures/initial_autocorrelation.png'));


% Trend Removal (First Differences)
firstDiffResult = diff(myData,1);
figure;
clf
plot(firstDiffResult)
hold on
plot(firstDiffResult,'.','markersize',6)
xlabel('t')
ylabel('x(t)')
title('Detrended time series by first differences smooth')
saveas(gcf,'partBb_figures/detrended_timeseries.png');
% set(gcf, 'Visible', 'off');

%% 2d - 3d scatter diagrams

delays = embeddelays(firstDiffResult,3,1);
plotd2d3(delays, 'Timeseries Scatter Plot');

%% Choose tau and m

% Detrended autocorrelation
% r=0 or r = 1/e
figure;
firstDiffautocorr = autocorrelation(firstDiffResult, Maxtau,'Detrended');
hold on;
plot([0 Maxtau+1],0*[1 1],'-','linewidth',0.5)
saveas(gcf,sprintf('partBb_figures/detrended_autocorrelation.png'));

% Mutual Information (first local minima)
figure;
mutM = mutualinformation(firstDiffResult, Maxtau, [],'','.-');
saveas(gcf,sprintf('partBb_figures/mutual_information.png'));
tau = 1;
mmax = 10;

% False Nearest Neighbors
figure;
fnnM = falsenearest(firstDiffResult,tau,mmax,[],[],'My');
saveas(gcf,sprintf('partBb_figures/fnn.png'));

%% Correlation dimension
m = 5;
[rcM,cM,rdM,dM,nuM] = correlationdimension(firstDiffResult,tau,m,'tau=1','m=5');

%% Prediction

numOfValidation = floor(0.4*dataLength);
numOfTraining = dataLength-numOfValidation;

k = 15;
q = 10;
Tmax = 20;

figure;
[nrmseV,preM] = localfitnrmse(firstDiffResult,tau,m,Tmax,k,q,' ');

figure;
[nrmseP,preP] = localpredictnrmse(firstDiffResult,numOfValidation,tau,m,Tmax,k,q,' ');