The simplest Singular Structure Analysis forecasting algorithm

Use one of the following data samples to show the forecast

Contents

file: demo_ssa_forecast

1) electricity consumption

x = [0.1925 0.2059 0.2731 0.4828 0.7077 0.9331 1.0521 1.0980 1.1000 1.0424 0.9528 0.9129 0.9097 0.8249 0.7598 0.7562 0.7005 0.7156 0.8270 0.8471 0.5891 0.3213 0.1987 0.1732 0.1466 0.1635 0.1892 0.3744 0.5850 0.7753 0.8808 0.9656 0.9297 0.8573 0.8851 0.8724 0.8489 0.8242 0.7763 0.7158 0.6584 0.6521 0.8567 0.8930 0.6392 0.3693 0.2284 0.1793 0.1726 0.1695 0.2098 0.4510 0.6292 0.8091 0.9150 0.9644 0.9509 0.9200 0.9153 0.8913 0.9090 0.9308 0.8675 0.7714 0.6928 0.7089 0.8377 0.8639 0.5720 0.3275 0.1999 0.1613 0.1352 0.1041 0.1456 0.3835 0.6100 0.7426 0.8700 0.9062 0.8766 0.8698 0.9330 0.9349 0.9033 0.8457 0.7573 0.6992 0.6422 0.6323 0.8158 0.8855 0.6103 0.3356 0.2118 0.1000]';
t = [733470 + 0.0417 *(1:length(x))]';
K = 24;   % period
M = 24*3; % forecast horizon

2) triangle example

% x = [1 2 3 2 1 2 3 2 1 2 3]';
% t = [1:length(x)]';
% K = 3;
% M = 6;

3) trapezoid example

% x = [0 0 1 1 0 0 -1 -1 0 0 1 1 0 0 -1 -1]';
% t = [1:length(x)]';
% K = 8;
% M = 10;

4) sine example

% t = linspace(-2*pi,2*pi, 160)';
% x = sin(t) + sin(4*t);
% K = 10;
% M = 120;

run the forecasting algorithm

x1 = ssaMtick(x,M,K); % see comments in the code

show the results

h=figure; hold('on');
t = [t; t(end)+((t(2)-t(1))*[1:M]')];
x = [x; NaN*ones(M,1)];
plot(t',x, 'b-');
plot(t',x1,'r-');
plot(t',x1,'r.');
plot(t',x, 'b.');
plot(t',x, 'b-');
legend('history', 'forecasting');
datetick('x','d')
ylabel('consumption');
xlabel('time');
axis tight
hold off
%saveas(h,'img/ssa_frc_consum.png','png');
close(h);
% end