DLM demo no 3, synthetic multivariate time series

Test the dlmsmo code with multivariate series with missing observations.

generate system matrices

[G,F] = dlmgensys(struct('order',2,'trig',2));

generate observations for the first series

m = size(G,2);
p = size(F,1);
nobs = 100;
t = (1:nobs)';

W = zeros(m,m); W(2,2) = 0.0004^2; for i=4:7 ; W(i,i)=0.0005^2; end
V = 0.8; % obs error std
x = zeros(nobs,m);
y = zeros(nobs,p);

x(1,:) = [0 0.0001 0.0003 1 1 2 1]; % initial values
for i=2:nobs
  x(i,:) = x(i-1,:)*G' + randn(1,m).*sqrt(diag(W))';
  y(i,:) = x(i,:)*F' + randn(1,p)*V;
end

generate second series

GG = kron(eye(2),G);
FF = kron(eye(2),F);
WW = diag([diag(W);diag(W)]);
VV = ones(nobs,2)*V;
yy = [y,y+5] + randn(nobs,2)*V;
x0 = zeros(m+m,1);
C0 = eye(m+m);

add some missing observations

yy(10,1) = NaN;
yy(50,:) = NaN;
yy(20:30,1) = NaN;
yy(end-9:end,2) = NaN;

dlm = dlmsmo(yy,FF,VV,x0,GG,WW,C0);

figure(1); clf
confband(t,dlm.x(1,:)',dlm.xstd(:,1));
hold on
confband(t,dlm.x(8,:)',dlm.xstd(:,8));
plot(t,yy,'.-')
hold off
title('two dimensional time serie with missing observations')
xlabel('time'); ylabel('y');

Published with MATLAB® R2018b